Semiclassical regime of Regge calculus and spin foams

International Nuclear Information System (INIS)

Bianchi, Eugenio; Satz, Alejandro

2009-01-01

Recent attempts to recover the graviton propagator from spin foam models involve the use of a boundary quantum state peaked on a classical geometry. The question arises whether beyond the case of a single simplex this suffices for peaking the interior geometry in a semiclassical configuration. In this paper we explore this issue in the context of quantum Regge calculus with a general triangulation. Via a stationary phase approximation, we show that the boundary state succeeds in peaking the interior in the appropriate configuration, and that boundary correlations can be computed order by order in an asymptotic expansion. Further, we show that if we replace at each simplex the exponential of the Regge action by its cosine-as expected from the semiclassical limit of spin foam models-then the contribution from the sign-reversed terms is suppressed in the semiclassical regime and the results match those of conventional Regge calculus

The contracted Bianchi identities in Regge calculus

International Nuclear Information System (INIS)

Williams, Ruth M

2012-01-01

In this note, we show explicitly how the linearized contracted Bianchi identities at a vertex in four-dimensional Regge calculus are related to a sum of the equations of motion for all the edges meeting at that vertex. (note)

Note on 3-dimensional Regge calculus

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Soda, Jiro

1991-01-01

We shall study 3-dimensional Regge calculus with concentrating the role of the Bianchi identity. As a result, the number of the physical variables is determined to be 12g - 12(g > 1). The reason why Rocek and Williams derived the exact result of Deser, Jackiw and 'tHooft is clarified. (author)

A new approach to the Regge calculus

International Nuclear Information System (INIS)

Porter, J.

1987-01-01

The paper develops a new approach to Regge calculus, a numerical technique used for the calculation of general relativistic spacetimes. The method is developed in an original '3 + 1' form in such a way that it can be applied to inhomogeneous spacetimes. (author)

Regge calculus and observations. II. Further applications

International Nuclear Information System (INIS)

Williams, R.M.; Ellis, G.F.R.

1983-03-01

The method, developed in an earlier paper, for tracing geodesics of particles and light rays through Regge calculus space-times, is applied to a number of problems in the Schwarschild geometry. It is possible to obtain accurate predictions of light-bending by taking sufficiently small Regge blocks. Calculations of perihelion precession, Thomas precession and the distortion of a ball of fluid moving on a geodesic can also show good agreement with the analytic solution. However difficulties arise in obtaining accurate predictions for general orbits in these space-times. Applications to other problems in general relativity are discussed briefly. (author)

Regge calculus and observations. II. Further applications.

Science.gov (United States)

Williams, Ruth M.; Ellis, G. F. R.

1984-11-01

The method, developed in an earlier paper, for tracing geodesies of particles and light rays through Regge calculus space-times, is applied to a number of problems in the Schwarzschild geometry. It is possible to obtain accurate predictions of light bending by taking sufficiently small Regge blocks. Calculations of perihelion precession, Thomas precession, and the distortion of a ball of fluid moving on a geodesic can also show good agreement with the analytic solution. However difficulties arise in obtaining accurate predictions for general orbits in these space-times. Applications to other problems in general relativity are discussed briefly.

The fundamental theorem of linearised Regge calculus

International Nuclear Information System (INIS)

Barrett, J.W.

1987-01-01

In linearised Regge calculus in a topologically trivial region, the space of linearised deviations of the edge lengths from a flat configuration, divided by the subspace of deformations due to translations of the vertices, is equivalent to the space of the linearised curvatures which satisfy the Bianchi identities. (orig.)

A new approach to the Regge calculus

International Nuclear Information System (INIS)

Porter, J.

1987-01-01

In paper 1 an original '3 + 1' form of Regge calculus was developed. In the current paper the method is tested by application to spherically symmetric vacuum space-times. Three different time slicing conditions are used and, where appropriate, the results are compared with the analytic solution with encouraging results. (author)

Time-evolution problem in Regge calculus

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Sorkin, R.

1975-01-01

The simplectic approximation to Einstein's equations (''Regge calculus'') is derived by considering the net to be actually a (singular) Riemannian manifold. Specific nets for open and closed spaces are introduced in terms of which one can formulate the general time-evolution problem, which thereby reduces to the repeated solution of finite sets of coupled nonlinear (algebraic) equations. The initial-value problem is also formulated in simplectic terms

On the combinatorial foundations of Regge-calculus

International Nuclear Information System (INIS)

Budach, L.

1989-01-01

Lipschitz-Killing curvatures of piecewise flat spaces are combinatorial analogues of Lipschitz-Killing curvatures of Riemannian manifolds. In the following paper rigorous combinatorial representations and proofs of all basic results for Lipschitz-Killing curvatures not using analytic arguments are given. The principal tools for an elementary representation of Regge calculus can be developed by means of basic properties of dihedral angles. (author)

The application of Regge calculus to quantum gravity and quantum field theory in a curved background

International Nuclear Information System (INIS)

Warner, N.P.

1982-01-01

The application of Regge calculus to quantum gravity and quantum field theory in a curved background is discussed. A discrete form of exterior differential calculus is developed, and this is used to obtain Laplacians for p-forms on the Regge manifold. To assess the accuracy of these approximations, the eigenvalues of the discrete Laplacians were calculated for the regular tesselations of S 2 and S 3 . The results indicate that the methods obtained in this paper may be used in curved space-times with an accuracy comparing with that obtained in lattice gauge theories on a flat background. It also becomes evident that Regge calculus provides particularly suitable lattices for Monte-Carlo techniques. (author)

The convergence of lattice solutions of linearised Regge calculus

International Nuclear Information System (INIS)

Barrett, J.W.; Williams, R.M.

1988-01-01

Sequences of configurations of linearised Regge calculus converging to plane wave solutions are constructed to illustrate an earlier result on convergence. It is shown that, for these examples, the convergence criterion filters out the solutions which do not satisfy Einstein's equations from those which do. (author)

Modified Regge calculus as an explanation of dark energy

International Nuclear Information System (INIS)

Stuckey, W M; McDevitt, T J; Silberstein, M

2012-01-01

Using the Regge calculus, we construct a Regge differential equation for the time evolution of the scale factor a(t) in the Einstein-de Sitter cosmology model (EdS). We propose two modifications to the Regge calculus approach: (1) we allow the graphical links on spatial hypersurfaces to be large, as in direct particle interaction when the interacting particles reside in different galaxies, and (2) we assume that luminosity distance D L is related to graphical proper distance D p by the equation D L = (1+z)√D p ·D p , where the inner product can differ from its usual trivial form. The modified Regge calculus model (MORC), EdS and ΛCDM are compared using the data from the Union2 Compilation, i.e. distance moduli and redshifts for type Ia supernovae. We find that a best fit line through logD L versus logz gives a correlation of 0.9955 and a sum of squares error (SSE) of 1.95. By comparison, the best fit ΛCDM gives SSE = 1.79 using H o = 69.2 kms -1 Mpc, Ω M = 0.29 and Ω Λ = 0.71. The best fit EdS gives SSE = 2.68 using H o 60.9 km s -1 Mpc. The best-fit MORC gives SSE = 1.77 and H o = 73.9 km s -1 Mpc using R = A -1 = 8.38 Gcy and m = 1.71 x 10 52 kg, where R is the current graphical proper distance between nodes, A -1 is the scaling factor from our non-trivial inner product, and m is the nodal mass. Thus, the MORC improves the EdS as well as ΛCDM in accounting for distance moduli and redshifts for type Ia supernovae without having to invoke accelerated expansion, i.e. there is no dark energy and the universe is always decelerating. (paper)

On the continuum limit of curvature squared actions in the Regge calculus

International Nuclear Information System (INIS)

Eliezer, D.

1989-01-01

We evaluate the continuum limit of a family of curvature squared actions for the Regge calculus proposed by Hamber and Williams. The answers depend on how the continuum limit is defined. When the link lengths are defined as the distance in an embedding space between the endpoints of the link, we find that no member of this family approaches the continuum limit correctly. Defining the link lengths as the length of a geodesic between the endpoints of the link, we find that a unique member is selected, and we prove for the general two dimensional compact manifold that this Regge calculus action converges to ∫R 2 √d d 2 x. (orig.)

A numerical study of the Regge calculus and smooth lattice methods on a Kasner cosmology

International Nuclear Information System (INIS)

Brewin, Leo

2015-01-01

Two lattice based methods for numerical relativity, the Regge calculus and the smooth lattice relativity, will be compared with respect to accuracy and computational speed in a full 3+1 evolution of initial data representing a standard Kasner cosmology. It will be shown that both methods provide convergent approximations to the exact Kasner cosmology. It will also be shown that the Regge calculus is of the order of 110 times slower than the smooth lattice method. (paper)

Calculation of relativistic model stars using Regge calculus

International Nuclear Information System (INIS)

Porter, J.

1987-01-01

A new approach to the Regge calculus, developed in a previous paper, is used in conjunction with the velocity potential version of relativistic fluid dynamics due to Schutz [1970, Phys. Rev., D, 2, 2762] to calculate relativistic model stars. The results are compared with those obtained when the Tolman-Oppenheimer-Volkov equations are solved by other numerical methods. The agreement is found to be excellent. (author)

A 3 + 1 Regge calculus model of the Taub universe

International Nuclear Information System (INIS)

Tuckey, P.A.

1988-01-01

The Piran and Williams [1986 Phys. Rev. D 33,1622] second-order formulation of 3 + 1 Regge calculus is used to calculate the evolution of a model of the Taub universe. The model displays qualitatively the correct behaviour, thereby giving some verification of the 3 + 1 formulation. (author)

On d=2 Regge calculus without triangulation

International Nuclear Information System (INIS)

Foerster, D.

1987-01-01

The supersymmetric version of a previously developed Regge calculus for d=2 euclidean gravity is given. In the context of string theory, a continuum theory is likely to exist for D<2 external space-time dimensions, just like in the bosonic case and essentially in agreement with the weak coupling regime D≤1 found by Gervais and Neveu for Liouville theory and its supersymmetric extension. The techniques developed here are intended to be of use, eventually, in lowering the critical dimensions of string theories. (orig.)

On the definition of the partition function in quantum Regge calculus

International Nuclear Information System (INIS)

Nishimura, Jun

1995-01-01

We argue that the definition of the partition function used recently to demonstrate the failure of Regge calculus is wrong. In fact, in the one-dimensional case, we show that there is a more natural definition, with which one can reproduce the correct results. (author)

Quantum Regge Calculus of Einstein-Cartan theory

International Nuclear Information System (INIS)

Xue Shesheng

2009-01-01

We study the Quantum Regge Calculus of Einstein-Cartan theory to describe quantum dynamics of Euclidean space-time discretized as a 4-simplices complex. Tetrad field e μ (x) and spin-connection field ω μ (x) are assigned to each 1-simplex. Applying the torsion-free Cartan structure equation to each 2-simplex, we discuss parallel transports and construct a diffeomorphism and local gauge-invariant Einstein-Cartan action. Invariant holonomies of tetrad and spin-connection fields along large loops are also given. Quantization is defined by a bounded partition function with the measure of SO(4)-group valued ω μ (x) fields and Dirac-matrix valued e μ (x) fields over 4-simplices complex.

Path integral in area tensor Regge calculus and complex connections

International Nuclear Information System (INIS)

Khatsymovsky, V.M.

2006-01-01

Euclidean quantum measure in Regge calculus with independent area tensors is considered using example of the Regge manifold of a simple structure. We go over to integrations along certain contours in the hyperplane of complex connection variables. Discrete connection and curvature on classical solutions of the equations of motion are not, strictly speaking, genuine connection and curvature, but more general quantities and, therefore, these do not appear as arguments of a function to be averaged, but are the integration (dummy) variables. We argue that upon integrating out the latter the resulting measure can be well-defined on physical hypersurface (for the area tensors corresponding to certain edge vectors, i.e. to certain metric) as positive and having exponential cutoff at large areas on condition that we confine ourselves to configurations which do not pass through degenerate metrics

On the area expectation values in area tensor Regge calculus in the Lorentzian domain

International Nuclear Information System (INIS)

Khatsymovsky, V.M.

2006-01-01

Wick rotation in area tensor Regge calculus is considered. The heuristical expectation is confirmed that the Lorentzian quantum measure on a spacelike area should coincide with the Euclidean measure at the same argument. The consequence is validity of probabilistic interpretation of the Lorentzian measure as well (on the real, i.e. spacelike areas)

Distributed mean curvature on a discrete manifold for Regge calculus

International Nuclear Information System (INIS)

Conboye, Rory; Miller, Warner A; Ray, Shannon

2015-01-01

The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector. (paper)

Distributed mean curvature on a discrete manifold for Regge calculus

Science.gov (United States)

Conboye, Rory; Miller, Warner A.; Ray, Shannon

2015-09-01

The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector.

A Kirchhoff-like conservation law in Regge calculus

International Nuclear Information System (INIS)

Gentle, Adrian P; Kheyfets, Arkady; McDonald, Jonathan R; Miller, Warner A

2009-01-01

Simplicial lattices provide an elegant framework for discrete spacetimes. The inherent orthogonality between a simplicial lattice and its circumcentric dual yields an austere representation of spacetime which provides a conceptually simple form of Einstein's geometric theory of gravitation. A sufficient understanding of simplicial spacetimes has been demonstrated in the literature for spacetimes devoid of all non-gravitational sources. However, this understanding has not been adequately extended to non-vacuum spacetime models. Consequently, a deep understanding of the diffeomorphic structure of the discrete theory is lacking. Conservation laws and symmetry properties are attractive starting points for coupling matter with the lattice. We present a simplicial form of the contracted Bianchi identity which is based on the E Cartan moment of rotation operator. This identity manifests itself in the conceptually simple form of a Kirchhoff-like conservation law. This conservation law enables one to extend Regge calculus to non-vacuum spacetimes and provides a deeper understanding of the simplicial diffeomorphism group.

On the two-dimensional model of quantum Regge gravity

International Nuclear Information System (INIS)

Khatsimovskij, V.M.

1991-01-01

The Ashtekar-like variables are introduced in the Regge calculus. A simplified model of the resulting theory is quantized canonically. The consequences related to quantization of Regge areas are obtained. 10 refs

The quantization of Regge calculus

International Nuclear Information System (INIS)

Rocek, M.; Williams, R.M.; Cambridge Univ.

1984-01-01

We discuss the quantization of Regge's discrete description of Einstein's theory of gravitation. We show how the continuum theory emerges in the weak field long wavelength limit. We also discuss reparametrizations and conformal transformations. (orig.)

A geometric construction of the Riemann scalar curvature in Regge calculus

International Nuclear Information System (INIS)

McDonald, Jonathan R; Miller, Warner A

2008-01-01

The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe is it ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a new fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a vertex-based weighted average of deficits per weighted average of dual areas

A geometric construction of the Riemann scalar curvature in Regge calculus

Science.gov (United States)

McDonald, Jonathan R.; Miller, Warner A.

2008-10-01

The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe is it ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a new fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a vertex-based weighted average of deficits per weighted average of dual areas.

Magnitude of regge cut contributions in the triple-regge region

International Nuclear Information System (INIS)

Bartels, J.; Kramer, G.

1976-09-01

Starting from the reggeon calculus, the various possibilities of absorptive Pomeron cut corrections in the triple-Regge region are considered. For the case of pp→pX, we estimate their importance at present day energies. We conclude that at highest ISR energies Pomeron cuts of the eikonal type are not enough, and enhanced diagrams with at least one additional triple Pomeron coupling need to be included. (orig.) [de

Null-strut calculus. II. Dynamics

International Nuclear Information System (INIS)

Kheyfets, A.; LaFave, N.J.; Miller, W.A.

1990-01-01

In this paper, we continue from the preceding paper to develop a fully functional Regge calculus geometrodynamic algorithm from the null-strut-calculus construction. The developments discussed include (a) the identification of the Regge calculus analogue of the constraint and evolution equations on the null-strut lattice, (b) a description of the Minkowski solid geometry for the simplicial blocks of the null-strut lattice, (c) a description of the evolution algorithm for the geometrodynamic scheme and an analysis of its consistency, and (d) a presentation of the dynamical degrees of freedom for a simplicial hypersurface and the description of an initial-value prescription. To demonstrate qualitatively this new approach to geometrodynamics, we present the most simple application of null-strut calculus that we know of---the Friedmann cosmology using the three-boundary of a 600-cell simplicial polytope to model the simplicial hypersurface

The geometry of classical Regge calculus

International Nuclear Information System (INIS)

Barrett, J.W.

1987-01-01

Standard notions of Riemannian geometry are applied to the case of piecewise-flat manifolds. Particular care is taken to explain how one may define some particular vectors and tensors in an invariant way at points of a conical singularity. The geometry surrounding the equations of motion and the energy-momentum of the piecewise-flat manifold is developed in detail. The resolution theorem is presented, which states that on certain resolution hypersurfaces there is a clear connection between the energy-momentum of the piecewise-flat manifold and the Regge equations of motion. (author)

Gluonic Regge singularities and anomalous dimensions in QCD

International Nuclear Information System (INIS)

Jaroszewicz, T.

1982-01-01

The Regge calculus results on the perturbative Pomeron are applied to deep inelastic scattering. Explicit expressions are given for the anomalous dimensions γsub(GGG)sup(n) and γsub(GF)sup(n) at n approx.= 1 to the lowest order in α and all orders in α/(n-1). (author)

Fixed-topology Lorentzian triangulations: Quantum Regge Calculus in the Lorentzian domain

Science.gov (United States)

Tate, Kyle; Visser, Matt

2011-11-01

A key insight used in developing the theory of Causal Dynamical Triangu-lations (CDTs) is to use the causal (or light-cone) structure of Lorentzian manifolds to restrict the class of geometries appearing in the Quantum Gravity (QG) path integral. By exploiting this structure the models developed in CDTs differ from the analogous models developed in the Euclidean domain, models of (Euclidean) Dynamical Triangulations (DT), and the corresponding Lorentzian results are in many ways more "physical". In this paper we use this insight to formulate a Lorentzian signature model that is anal-ogous to the Quantum Regge Calculus (QRC) approach to Euclidean Quantum Gravity. We exploit another crucial fact about the structure of Lorentzian manifolds, namely that certain simplices are not constrained by the triangle inequalities present in Euclidean signa-ture. We show that this model is not related to QRC by a naive Wick rotation; this serves as another demonstration that the sum over Lorentzian geometries is not simply related to the sum over Euclidean geometries. By removing the triangle inequality constraints, there is more freedom to perform analytical calculations, and in addition numerical simulations are more computationally efficient. We first formulate the model in 1 + 1 dimensions, and derive scaling relations for the pure gravity path integral on the torus using two different measures. It appears relatively easy to generate "large" universes, both in spatial and temporal extent. In addition, loopto-loop amplitudes are discussed, and a transfer matrix is derived. We then also discuss the model in higher dimensions.

Null-strut calculus. I. Kinematics

International Nuclear Information System (INIS)

Kheyfets, A.; LaFave, N.J.; Miller, W.A.

1990-01-01

This paper describes the kinematics of null-strut calculus---a 3+1 Regge calculus approach to general relativity. We show how to model the geometry of spacetime with simplicial spacelike three-geometries (TET's) linked to ''earlier'' and ''later'' momentumlike lattice surfaces (TET * ) entirely by light rays or ''null struts.'' These three-layered lattice spacetime geometries are defined and analyzed using combinatorial formulas for the structure of polytopes. The following paper in this series describes how these three-layered spacetime lattices are used to model spacetimes in full conformity with Einstein's theory of gravity

A few insights into the nature of classical and quantum gravity via null-strut calculus

International Nuclear Information System (INIS)

Kheyfets, Arkady

1989-01-01

Null-strut calculus is a 3 + 1 formulation of standard Regge calculus, wherein the dynamics of 3-geometry is propagated in time along light rays, or 'null struts'. However, just as Regge calculus is a discrete and geometric tool for the description of Einstein's theory of gravitation, so too NSC offers itself as a discrete and geometric tool for the description of Einstein's spacetime as the dynamics of discrete spacelike 3-geometries in time, or discrete geometrodynamics. It has for its objectives to provide a discrete model of a 3 + 1 split of spacetime into space plus time, while in so doing to preserve and illuminate the geometric content of Einstein's theory of gravity. The feature of 'light-cone-produced duality' is central to null-strut calculus. This paper will capitalise on this feature, and will attempt to provide some insights into the nature of classical and quantum gravity. (Author)

Regge phenomena

International Nuclear Information System (INIS)

Michael, C.

1975-01-01

Many features of data on high scattering can be best understood from a complex angular momentum or Regge approach. The Regge pole approach as such has had a history of alternating periods of excessive popularity and of rejection. It is thus worthwhile to review the field as it stands at present and to highlight the simple insights given by a Regge pole approach and also to bring out some of the complications such as those which lead to Regge cuts. As well as its tried and tested value in discussing two body and quasi-two body scattering, Regge pole language has much to give to multiparticle scattering and this is sketched in the last section. (author)

Fast algorithms for computing defects and their derivatives in the Regge calculus

International Nuclear Information System (INIS)

Brewin, Leo

2011-01-01

Any practical attempt to solve the Regge equations, these being a large system of non-linear algebraic equations, will almost certainly employ a Newton-Raphson-like scheme. In such cases, it is essential that efficient algorithms be used when computing the defect angles and their derivatives with respect to the leg lengths. The purpose of this paper is to present details of such an algorithm.

Gribov's reggeon calculus: its physical basis and implications

International Nuclear Information System (INIS)

Baker, M.; Ter-Martirosyan, K.A.

1976-01-01

The equations of Gribov's Reggeon calculus and the cutting rules of Abramovskii, Gribov and Kancheli are derived from the assumption that processes involving large virtual masses are damped. The discussion is carried out entirely in the s channel and no use is made of the details of any particular field theory. Both the mathematical development and the physical picture which evolves rest on the assumed multiperipheral origin of Regge behavior. (Auth.)

Basic Regge theory rides again

International Nuclear Information System (INIS)

Johnson, R.C.

1979-01-01

In this series of lectures Regge theory, which plays a role in high-energy production just as in 2 → 2 processes, is considered. It is shown that exclusive applications and tests are hampered by lack of events and phase space but observation of double Pomeron exchange is encouraging for the multi-Regge Model. In inclusive processes, approximate scaling and its approach are described, including development of a central plateau and limiting fragmentation and triple-Regge behaviour. The Regge picture also sets a natural scale of distance in rapidity for discussion of interparticle correlations. All this understanding involves domination of unphysical multiparticle forward amplitudes by the familiar factorising Regge poles seen directly in 2 → 2 reactions. (UK)

Inclusive central region in perturbative Reggeon calculus

International Nuclear Information System (INIS)

Pajares, C.; Pascual, R.

1976-01-01

The single-particle inclusive cross section and the correlation function are studied in the perturbative approach to Gribov's Reggeon calculus; the leading contributions to both functions are evaluated. The large energy rise of the inclusive cross section appears as a consequence of the Pomerons having an intercept larger than 1. The same set of parameters which describes correctly the cross-section data and the triple-Regge region also describes the inclusive data in the central region

The analytic foundations of Regge theory

International Nuclear Information System (INIS)

White, A.R.

1976-01-01

Regge poles were first introduced into relativistic scattering theory nearly fifteen years ago. The necessity for accompanying Regge cuts was discovered within two years. The intervening years have seen a gradual improvement of our understanding of Regge theory, but, particularly at the multiparticle level, the theory has remained incomplete with its fundamental status unclear. However, on the basis of recent progress a complete and systematic development of the Regge theory of elastic and multiparticle amplitude is given. (Auth.)

Overlap function and Regge cut in a self-consistent multi-Regge model

International Nuclear Information System (INIS)

Banerjee, H.; Mallik, S.

1977-01-01

A self-consistent multi-Regge model with unit intercept for the input trajectory is presented. Violation of unitarity is avoided in the model by assuming the vanishing of the pomeron-pomeron-hadron vertex, as the mass of either pomeron tends to zero. The model yields an output Regge pole in the inelastic overlap function which for t>0 lies on the r.h.s. of the moving branch point in the complex J-plane, but for t<0 moves to unphysical sheets. The leading Regge-cut contribution to the forward diffraction amplitude can be negative, so that the total cross section predicted by the model attains a limiting value from below

Overlap function and Regge cut in a self-consistent multi-Regge model

Energy Technology Data Exchange (ETDEWEB)

Banerjee, H [Saha Inst. of Nuclear Physics, Calcutta (India); Mallik, S [Bern Univ. (Switzerland). Inst. fuer Theoretische Physik

1977-04-21

A self-consistent multi-Regge model with unit intercept for the input trajectory is presented. Violation of unitarity is avoided in the model by assuming the vanishing of the pomeron-pomeron-hadron vertex, as the mass of either pomeron tends to zero. The model yields an output Regge pole in the inelastic overlap function which for t>0 lies on the r.h.s. of the moving branch point in the complex J-plane, but for t<0 moves to unphysical sheets. The leading Regge-cut contribution to the forward diffraction amplitude can be negative, so that the total cross section predicted by the model attains a limiting value from below.

Analytic structure of the n=7 scattering amplitude in N=4 SYM theory at multi-Regge kinematics. Conformal Regge pole contribution

Energy Technology Data Exchange (ETDEWEB)

Bartels, Jochen; Kormilitzin, Andrey [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Lipatov, Lev [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; St. Petersburg Nuclear Physics Institute, St. Petersburg (Russian Federation)

2013-11-15

We investigate the analytic structure of the 2 {yields} 5 scattering amplitude in the planar limit of N=4 SYM in multi-Regge kinematics in all physical regions. We demonstrate the close connection between Regge pole and Regge cut contributions: in a selected class of kinematic regions (Mandelstam regions) the usual factorizing Regge pole formula develops unphysical singularities which have to be absorbed and compensated by Regge cut contributions. This leads, in the corrections to the BDS formula, to conformal invariant 'renormalized' Regge pole expressions in the remainder function. We compute these renormalized Regge poles for the 2 {yields} 5 scattering amplitude.

Classical models for Regge trajectories

International Nuclear Information System (INIS)

Biedenharn, L.C.; Van Dam, H.; Marmo, G.; Morandi, G.; Mukunda, N.; Samuel, J.; Sudarshan, E.C.G.

1987-01-01

Two classical models for particles with internal structure and which describe Regge trajectories are developed. The remarkable geometric and other properties of the two internal spaces are highlighted. It is shown that the conditions of positive time-like four-velocity and energy momentum for the classical system imply strong and physically reasonable conditions on the Regge mass-spin relationship

Non-Regge and hyper-Regge effects in pion-nucleon charge exchange scattering at high energies

International Nuclear Information System (INIS)

Joynson, D.; Leader, E.; Nicolescu, B.; Paris-6 Univ., 75; Lopez, C.

1975-04-01

The experimental data on the charge exchange differential cross-section and on the difference on the π + p and π - p total cross-sections between 5GeV/c to 200GeV/c are shown to be incompatible with conventional Regge asymptotic behavior. It is shown that an additional term is required which grows in importance with energy. The precise form of the new term cannot be ascertained, but it is shown that it corresponds to a singularity at J=1 in the complex angular momentum plane. Amongst the possible types of additional term there are two which have been closely analysed: a non-Regge behavior, a hyper-Regge term which have allowed very striking predictions in particular for the charge exchange polarisation [fr

Construction of multi-Regge amplitudes by the Van Hove--Durand method

International Nuclear Information System (INIS)

Morrow, R.A.

1978-01-01

The Van Hove--Durand method of deriving Regge amplitudes by summing Feynman tree diagrams is extended to the multi-Regge domain. Using previously developed vertex functions for particles of arbitrary spins, single-, double-, and triple-Regge amplitudes incorporating signature are obtained. Criteria necessary to arrive at unique Regge-pole terms are found. It is also shown how external spins can be included

Heptagon amplitude in the multi-Regge regime

International Nuclear Information System (INIS)

Bartels, J.

2014-05-01

As we have shown in previous work, the high energy limit of scattering amplitudes in N=4 supersymmetric Yang-Mills theory corresponds to the infrared limit of the 1-dimensional quantum integrable system that solves minimal area problems in AdS 5 . This insight can be developed into a systematic algorithm to compute the strong coupling limit of amplitudes in the multi-Regge regime through the solution of auxiliary Bethe Ansatz equations. We apply this procedure to compute the scattering amplitude for n=7 external gluons in different multi-Regge regions at infinite 't Hooft coupling. Our formulas are remarkably consistent with the expected form of 7-gluon Regge cut contributions in perturbative gauge theory. A full description of the general algorithm and a derivation of results is given in a forthcoming paper.

Towards understanding Regge trajectories in holographic QCD

International Nuclear Information System (INIS)

Cata, Oscar

2007-01-01

We reassess a work done by Migdal on the spectrum of low-energy vector mesons in QCD in the light of the anti-de Sitter (AdS)-QCD correspondence. Recently, a tantalizing parallelism was suggested between Migdal's work and a family of holographic duals of QCD. Despite the intriguing similarities, both approaches face a major drawback: the spectrum is in conflict with well-tested Regge scaling. However, it has recently been shown that holographic duals can be modified to accommodate Regge behavior. Therefore, it is interesting to understand whether Regge behavior can also be achieved in Migdal's approach. In this paper we investigate this issue. We find that Migdal's approach, which is based on a modified Pade approximant, is closely related to the issue of quark-hadron duality breakdown in QCD

Analytic structure of the n=7 scattering amplitude in N=4 SYM theory in multi-Regge kinematics. Conformal Regge cut contribution

International Nuclear Information System (INIS)

Bartels, Jochen; Kormilitzin, Andrey; Oxford Univ.; Lipatov, Lev N.; Oxford Univ.; St. Petersburg State Univ.

2014-11-01

In this second part of our investigation of the analytic structure of the 2→5 scattering amplitude in the planar limit of N=4 SYM in multi-Regge kinematics we compute, in all kinematic regions, the Regge cut contributions in leading order. The results are infrared finite and conformally invariant.

Factorization of the six-particle multi-Regge amplitude

International Nuclear Information System (INIS)

Moen, I.O.

1975-01-01

It is shown that factorization of the multi-Regge contribution to the six-particle amplitude follows from the complex-helicity-plane structure, the Steinmann relations, and extended unitarity. The six-particle multi-Regge amplitude also satisfies some new discontinuity relations which are interpreted as resulting from the interplay of singularities required by the Gram-determinant constraint in four-dimensional space-time

Multi-Regge limit of the n-gluon bubble ansatz

Energy Technology Data Exchange (ETDEWEB)

Bartels, J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Schomerus, V.; Sprenger, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2012-07-15

We investigate n-gluon scattering amplitudes in the multi-Regge region of N=4 supersymmetric Yang-Mills theory at strong coupling. Through a careful analysis of the thermodynamic bubble ansatz (TBA) for surfaces in AdS{sub 5} with n-g(lu)on boundary conditions we demonstrate that the multi-Regge limit probes the large volume regime of the TBA. In reaching the multi-Regge regime we encounter wall-crossing in the TBA for all n>6. Our results imply that there exists an auxiliary system of algebraic Bethe ansatz equations which encode valuable information on the analytical structure of amplitudes at strong coupling.

Regge asymptotics of scattering with flavour exchange in QCD

International Nuclear Information System (INIS)

Kirschner, R.

1994-06-01

The contribution to the perturbative Regge asymptotics of the exchange of two reggeized fermions with opposite helicity is investigated. The methods of conformal symmetry known for the case of gluon exchange are extended to this case where double-logarithmic contributions dominate the asymptotics. The Regge trajectories at large momentum transfer are calculated. (orig.)

Path integral measure and triangulation independence in discrete gravity

Science.gov (United States)

Dittrich, Bianca; Steinhaus, Sebastian

2012-02-01

A path integral measure for gravity should also preserve the fundamental symmetry of general relativity, which is diffeomorphism symmetry. In previous work, we argued that a successful implementation of this symmetry into discrete quantum gravity models would imply discretization independence. We therefore consider the requirement of triangulation independence for the measure in (linearized) Regge calculus, which is a discrete model for quantum gravity, appearing in the semi-classical limit of spin foam models. To this end we develop a technique to evaluate the linearized Regge action associated to Pachner moves in 3D and 4D and show that it has a simple, factorized structure. We succeed in finding a local measure for 3D (linearized) Regge calculus that leads to triangulation independence. This measure factor coincides with the asymptotics of the Ponzano Regge Model, a 3D spin foam model for gravity. We furthermore discuss to which extent one can find a triangulation independent measure for 4D Regge calculus and how such a measure would be related to a quantum model for 4D flat space. To this end, we also determine the dependence of classical Regge calculus on the choice of triangulation in 3D and 4D.

Regge poles and alpha scattering

International Nuclear Information System (INIS)

Ceuleneer, R.

1974-01-01

The direct Regge pole model as a means of describing resonances in elastic particle scattering has been used for the analysis of the so-called ''anormalous large angle scattering'' of alpha particles by spinless nuclei. (Z.M.)

Tensor Calculus: Unlearning Vector Calculus

Science.gov (United States)

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-01-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

High energy production of gluons in a quasi-multi-Regge kinematics

International Nuclear Information System (INIS)

Fadin, V.S.; Lipatov, L.N.

1989-01-01

Inelastic gluon-gluon scattering amplitudes in the Born approximation for the quasi-multi-Regge kinematics are calculated, starting with the Veneziano-type expression for the inelastic amplitude of the gluon-tachyon scattering with its subsequent simplification in the region of large energies and the Regge slope α'→0. Results obtained allow one to determine the high order corrections to the gluon Regge trajectory, the reggeon-particle vertices and to the integral kernel of the Bethe-Salpeter equation for the vacuum t-channel partial waves. 10 refs.; 7 figs

Regge trajectories for heavy quarkonia from the quadratic form of the spinless Salpeter-type equation

Science.gov (United States)

Chen, Jiao-Kai

2018-03-01

In this paper, we present one new form of the Regge trajectories for heavy quarkonia which is obtained from the quadratic form of the spinless Salpeter-type equation (QSSE) by employing the Bohr-Sommerfeld quantization approach. The obtained Regge trajectories take the parameterized form M^2={β }({c_l}l+{π }n_r+c_0)^{2/3}+c_1, which are different from the present Regge trajectories. Then we apply the obtained Regge trajectories to fit the spectra of charmonia and bottomonia. The fitted Regge trajectories are in good agreement with the experimental data and the theoretical predictions.

Radial and Regge excitations in unified, grand unified and subconstituent models

International Nuclear Information System (INIS)

Schnitzer, H.J.

1981-01-01

Necessary group theoretic conditions for all elementary gauge bosons and fermions of an arbitrary renormalizable gauge theory to lie on Regge trajectories are reviewed. It is then argued that in properly unified gauge theories all particles of a given spin lie on Regge trajectories. This then implies that a properly unified gauge theory has no local U(1) factor groups, and no massive fermion singlets. A consideration of the general pattern of Regge and radial recurrences to be expected in quantum field theories suggests that the presence or absence of spin 3/2 quarks and/or leptons in the TeV region will provide crucial clues to enable one to distinguish between various classes of unified, grand unified, and subconstituent models. The correct interpretation of such excited fermions will require correlation with the higgs boson mass and possible radial and Regge excitations of the weak vector bosons. (orig.)

Regge-plus-resonance predictions for charged-kaon photoproduction from the deuteron

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Van Cauteren T.

2010-04-01

Full Text Available We present a Regge-inspired effective-Lagrangian framework for charged-kaon photoproduction from the deuteron. Quasi-free kaon production is investigated using the Regge-plus-resonance elementary operator within the non-relativistic plane-wave impulse approximation. The Regge-plus-resonance model was developed to describe photoinduced and electroinduced kaon production off protons and can be extended to strangeness production off neutrons. The non-resonant contributions to the amplitude are modelled in terms of K+ (494 and K*+ (892 Regge-trajectory exchange in the t-channel. This amplitude is supplemented with a selection of s-channel resonance-exchange diagrams. We investigate several sources of theoretical uncertainties on the semi-inclusive charged-kaon production cross section. The experimental error bars on the photocoupling helicity amplitudes turn out to put severe limits on the predictive power when considering quasi-free kaon production on a bound neutron.

Superstring elastic scattering at √s≥1019 GeV. The covariant loop calculus approach

International Nuclear Information System (INIS)

Bellini, A.; Cristofano, G.; Fabbrichesi, M.; Roland, K.; Texas Univ., Austin, TX

1990-01-01

We study quantum gravity by considering the elastic scattering of two on-shell string ground states in the large s, fixed t asymptotic limit. The amplitude is computed by means of the covariant loop calculus which turns out to be a powerful method in the study of such a Regge regime. The leading contribution in powers of s is shown to factorize at any g-loop order in a product of g+1 tree amplitudes times the expectation value of a factorized operator. The cumulative effect of these contributions - once it has been resummed - restores unitarity in the theory and gives a deflection angle in agreement with the linear approximation to general relativity. In the process, it is possible to determine the normalization dictated by unitarity of all terms in the topological expansion. Next, the first sub-leading contribution is calculated at the two-loop order, the so-called H-diagram. A resummation of such terms gives rise to the first non-linear correction in the deflection angle. Our results are in agreement with previous work by Amati, Ciafaloni and Veneziano in the framework of Regge-Gribov techniques. The correspondence between the two approaches is discussed. (orig.)

Wilson loop OPE, analytic continuation and multi-Regge limit

International Nuclear Information System (INIS)

Hatsuda, Yasuyuki

2014-05-01

We explore a direct connection between the collinear limit and the multi-Regge limit for scattering amplitudes in the N=4 super Yang-Mills theory. Starting with the collinear expansion for the six-gluon amplitude in the Euclidean kinematic region, we perform an analytic continuation term by term to the so-called Mandelstam region. We find that the result coincides with the collinear expansion of the analytically continued amplitude. We then take the multi-Regge limit, and conjecture that the final result precisely reproduces the one from the BFKL approach. Combining this procedure with the OPE for null polygonal Wilson loops, we explicitly compute the leading contribution in the ''collinear-Regge'' limit up to five loops. Our results agree with all the known results up to four loops. At five-loop, our results up to the next-to-next-to-leading logarithmic approximation (NNLLA) also reproduce the known results, and for the N 3 LLA and the N 4 LLA give non-trivial predictions. We further present an all-loop prediction for the imaginary part of the next-to-double-leading logarithmic approximation. Our procedure has a possibility of an interpolation from weak to strong coupling in the multi-Regge limit with the help of the OPE.

Regge cuts: A general approach

International Nuclear Information System (INIS)

Weis, J.H.

1976-01-01

We discuss an approach to the calculation of Regge-cut contributions to scattering amplitudes which relies only on the general structure of the physical Reggeon couplings. It thus allows a unified treatment of disparate models [such as the Feynman (Mandelstam) graph model and the dual model] and a general derivation of the Abramovskii--Gribov--Kancheli (AGK) rules. The structure of the Reggeon couplings is expressed through integrals over complex helicity. The Regge-cut amplitude can then be obtained, and its s-channel discontinuity, taken; there results a direct derivation of a set of ''cutting rules'' which express the total discontinuity as a sum of terms involving various discontinuities of the Reggeon couplings. The equality of these discontinuities follows directly if the singularities in complex helicity are the usual ones. Thus the AGK rules are seen to be quite model independent. Here we study in detail the simplest example: the Reggeon-particle cut in the four-particle amplitude

Analytic multi-Regge theory and the pomeron in QCD. 1

International Nuclear Information System (INIS)

White, A.R.

1991-01-01

This paper reports on the formalism of analytic multi-Regge theory developed as a basis for the study of abstract critical and super-critical pomeron high-energy behavior and for related studies of the Regge behavior of spontaneously broken gauge theories and the pomeron in QCD. Asymptotic domains of analyticity for multiparticle amplitudes are shown to follow from properties of field theory and S-matrix theory. General asymptotic dispersion relations are then derived for such amplitudes in which the spectral components are described by the graphical formalism of hexagraphs. Further consequences are distinct Sommerfeld-Watson representations for each hexagraph spectral component, together with a complete set of angular momentum plane unitarity equations which control the form of all multi-Regge amplitudes. Because of this constraint of reggeon unitarity the critical pomeron solution of the reggeon field theory gives the only known non-trivial unitary high-energy S-matrix. By exploiting the full structure of multi-Regge amplitudes as the pomeron becomes super-critical, one can study the simultaneous modification of hadrons and the pomeron. The result is a completely consistent description of the super-critical pomeron appearing in hadron scattering. Reggeon unitarity is satisfied in the super-critical phase by the appearance of a massive gluon (Reggeized vector particle) coupling pair-wise to the pomeron

Calculus

CERN Document Server

Jones, Patrick

2014-01-01

Practice makes perfect-and helps deepen your understanding of calculus 1001 Calculus Practice Problems For Dummies takes you beyond the instruction and guidance offered in Calculus For Dummies, giving you 1001 opportunities to practice solving problems from the major topics in your calculus course. Plus, an online component provides you with a collection of calculus problems presented in multiple-choice format to further help you test your skills as you go. Gives you a chance to practice and reinforce the skills you learn in your calculus courseHelps you refine your understanding of calculusP

Semiclassical approach to Regge poles trajectories calculations for nonsingular potentials: Thomas-Fermi type

International Nuclear Information System (INIS)

Belov, S M; Avdonina, N B; Felfli, Z; Marletta, M; Msezane, A Z; Naboko, S N

2004-01-01

A simple semiclassical approach, based on the investigation of anti-Stokes line topology, is presented for calculating Regge poles for nonsingular (Thomas-Fermi type) potentials, namely potentials with singularities at the origin weaker than order -2. The anti-Stokes lines for Thomas-Fermi potentials have a more complicated structure than those of singular potentials and require careful application of complex analysis. The explicit solution of the Bohr-Sommerfeld quantization condition is used to obtain approximate Regge poles. We introduce and employ three hypotheses to obtain several terms of the Regge pole approximation

Approximation of hadron interactions by Regge diagrams with multipomeron exchange

International Nuclear Information System (INIS)

Barashenkov, V.S.

1988-01-01

A good agreement of hadron diffraction interaction total cross section and their elastic scattering at small angles calculated by summarizing Regge multipomeron exchange diagrams with experiment mentioned by a number of authors results from the fitting of a great variety of the parameters contained in the formulas. The agreement of the other hadron characteristcs with experiment is worse. Distribution of hadron interactions over the number of fragmenting quark-gluon strings calculated by utilizing Regge diagrams is discussed

Conditional probabilities in Ponzano-Regge minisuperspace

International Nuclear Information System (INIS)

Petryk, Roman; Schleich, Kristin

2003-01-01

We examine the Hartle-Hawking no-boundary initial state for the Ponzano-Regge formulation of gravity in three dimensions. We consider the behavior of conditional probabilities and expectation values for geometrical quantities in this initial state for a simple minisuperspace model consisting of a two-parameter set of anisotropic geometries on a 2-sphere boundary. We find dependence on the cutoff used in the construction of Ponzano-Regge amplitudes for expectation values of edge lengths. However, these expectation values are cutoff independent when computed in certain, but not all, conditional probability distributions. Conditions that yield cutoff independent expectation values are those that constrain the boundary geometry to a finite range of edge lengths. We argue that such conditions have a correspondence to fixing a range of local time, as classically associated with the area of a surface for spatially closed cosmologies. Thus these results may hint at how classical spacetime emerges from quantum amplitudes

Bounds for OPE coefficients on the Regge trajectory

Science.gov (United States)

Costa, Miguel S.; Hansen, Tobias; Penedones, João

2017-10-01

We consider the Regge limit of the CFT correlation functions and , where J is a vector current, T is the stress tensor and O is some scalar operator. These correlation functions are related by a type of Fourier transform to the AdS phase shift of the dual 2-to-2 scattering process. AdS unitarity was conjectured some time ago to be positivity of the imaginary part of this bulk phase shift. This condition was recently proved using purely CFT arguments. For large N CFTs we further expand on these ideas, by considering the phase shift in the Regge limit, which is dominated by the leading Regge pole with spin j( ν), where ν is a spectral parameter. We compute the phase shift as a function of the bulk impact parameter, and then use AdS unitarity to impose bounds on the analytically continued OPE coefficients {C}_JJ}j(ν )} and C TTj(ν) that describe the coupling to the leading Regge trajectory of the current J and stress tensor T. AdS unitarity implies that the OPE coefficients associated to non-minimal couplings of the bulk theory vanish at the intercept value ν = 0, for any CFT. Focusing on the case of large gap theories, this result can be used to show that the physical OPE coefficients {C}_{JJT and C TTT , associated to non-minimal bulk couplings, scale with the gap Δ g as Δ g - 2 or Δ g - 4 . Also, looking directly at the unitarity condition imposed at the OPE coefficients {C_JJT and C TTT results precisely in the known conformal collider bounds, giving a new CFT derivation of these bounds. We finish with remarks on finite N theories and show directly in the CFT that the spin function j( ν) is convex, extending this property to the continuation to complex spin.

N=4 supersymmetric Yang Mills scattering amplitudes at high energies. The Regge cut contribution

International Nuclear Information System (INIS)

Bartels, J.; Sabio Vera, A.

2008-07-01

We further investigate, in N=4 supersymmetric Yang Mills theories, the high energy Regge behavior of six-point scattering amplitudes. In particular, for the new Regge cut contribution found in our previous paper, we compute in the leading logarithmic approximation (LLA) the energy spectrum of the BFKL equation in the color octet channel, and we calculate explicitly the two loop corrections to the discontinuities of the amplitudes for the transitions 2→4 and 3→3. We find an explicit solution of the BFKL equation for the octet channel for arbitrary momentum transfers and investigate the intercepts of the Regge singularities in this channel. As an important result we find that the universal collinear and infrared singularities of the BDS formula are not affected by this Regge-cut contribution. (orig.)

Mean multiplicity in the Regge models with rising cross sections

International Nuclear Information System (INIS)

Chikovani, Z.E.; Kobylisky, N.A.; Martynov, E.S.

1979-01-01

Behaviour of the mean multiplicity and the total cross section σsub(t) of hadron-hadron interactions is considered in the framework of the Regge models at high energies. Generating function was plotted for models of dipole and froissaron, and the mean multiplicity and multiplicity moments were calculated. It is shown that approximately ln 2 S (energy square) in the dipole model, which is in good agreement with the experiment. It is also found that in various Regge models approximately σsub(t)lnS

Phase space descriptions for simplicial 4D geometries

International Nuclear Information System (INIS)

Dittrich, Bianca; Ryan, James P

2011-01-01

Starting from the canonical phase space for discretized (4D) BF theory, we implement a canonical version of the simplicity constraints and construct phase spaces for simplicial geometries. Our construction allows us to study the connection between different versions of Regge calculus and approaches using connection variables, such as loop quantum gravity. We find that on a fixed triangulation the (gauge invariant) phase space associated with loop quantum gravity is genuinely larger than the one for length and even area Regge calculus. Rather, it corresponds to the phase space of area-angle Regge calculus, as defined in [1] (prior to the imposition of gluing constraints, which ensure the metricity of the triangulation). Finally, we show that for a subclass of triangulations one can construct first-class Hamiltonian and diffeomorphism constraints leading to flat 4D spacetimes.

Regge-pole description of potential scattering by means of the phase-integral method

International Nuclear Information System (INIS)

Amaha, A.

1992-01-01

The application of Regge-pole theory to different atomic and molecular scattering has shown to have promising interpretational power in the differential cross sections. Differential cross sections can be analysed in terms of interference between the 'background' amplitude and a few Regge-pole positions of the scattering matrix (S matrix) representing surface waves around the interaction region. By the analytic continuation of the radial Schroedinger differential equation into the complex plane of angular momentum one can determine the analytic properties of the S matrix which contains the physical information in the scattering processes. For interaction potentials fulfilling certain properties, the study of the S matrix leads to the study of the F matrix introduced by Froeman and Froeman for the treatment of connection problems for phase-integral solutions of the differential equation. In this thesis the quantum mechanical scattering problem is analysed in the framework of Regge-pole theory with the use of the complex-angular-momentum formalism. To determine the S matrix, the relevant F matrix elements which give the stokes constants are derived and their properties are studied. The poles of the S matrix for particular complex values of the angular momentum quantum number are the Regge-poles. Using the Regge-pole positions and residues together with the background integral, the differential cross sections are calculated and compared with corresponding partial-wave representations

Effective action for the Regge processes in gravity

Energy Technology Data Exchange (ETDEWEB)

Lipatov, L.N. [Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg (Russian Federation); Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

2011-05-15

It is shown, that the effective action for the reggeized graviton interactions can be formulated in terms of the reggeon fields A{sup ++} and A{sup --} and the metric tensor g{sub {mu}}{sub {nu}} in such a way, that it is local in the rapidity space and has the property of general covariance. The corresponding effective currents j{sup -} and j{sup +} satisfy the Hamilton-Jacobi equation for a massless particle moving in the gravitational field. These currents are calculated explicitly for the shock wave-like fields and a variation principle for them is formulated. As an application, we reproduce the effective lagrangian for the multi-regge processes in gravity together with the graviton Regge trajectory in the leading logarithmic approximation with taking into account supersymmetric contributions. (orig.)

MHV amplitudes for 3→3 gluon scattering in Regge limit

International Nuclear Information System (INIS)

Bartels, J.; Prygarin, A.

2010-12-01

We calculate corrections to the BDS formula for the six-particle planar MHV amplitude for the gluon transition 3 → 3 in the multi-Regge kinematics for the physical region, in which the Regge pole ansatz is not valid. The remainder function at two loops is obtained by an analytic continuation of the expression derived by Goncharov, Spradlin, Vergu and Volovich to the kinematic region described by the Mandelstam singularity exchange in the crossing channel. It contains both the imaginary and real contributions being in agreement with the BFKL predictions. The real part of the three loop expression is found from a dispersion-like all-loop formula for the remainder function in the multi-Regge kinematics derived by one of the authors. We also make a prediction for the all-loop real part of the remainder function multiplied by the BDS phase, which can be accessible through calculations in the regime of the strong coupling constant. (orig.)

MHV amplitudes for 3{yields}3 gluon scattering in Regge limit

Energy Technology Data Exchange (ETDEWEB)

Bartels, J.; Prygarin, A. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Lipatov, L.N. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; St. Petersburg Nuclear Physics Institute (Russian Federation)

2010-12-15

We calculate corrections to the BDS formula for the six-particle planar MHV amplitude for the gluon transition 3 {yields} 3 in the multi-Regge kinematics for the physical region, in which the Regge pole ansatz is not valid. The remainder function at two loops is obtained by an analytic continuation of the expression derived by Goncharov, Spradlin, Vergu and Volovich to the kinematic region described by the Mandelstam singularity exchange in the crossing channel. It contains both the imaginary and real contributions being in agreement with the BFKL predictions. The real part of the three loop expression is found from a dispersion-like all-loop formula for the remainder function in the multi-Regge kinematics derived by one of the authors. We also make a prediction for the all-loop real part of the remainder function multiplied by the BDS phase, which can be accessible through calculations in the regime of the strong coupling constant. (orig.)

Solving QCD via multi-Regge theory

International Nuclear Information System (INIS)

White, A. R.

1998-01-01

A high-energy, transverse momentum cut-off, solution of QCD is outlined. Regge pole and single gluon properties of the pomeron are directly related to the confinement and chiral symmetry breaking properties of the hadron spectrum. This solution, which corresponds to a supercritical phase of Reggeon Field Theory, may only be applicable to QCD with a very special quark content

On the regge-cut cancellation in planar amplitude of the dual unitarisation scheme

International Nuclear Information System (INIS)

Kwiecinski, J.; Sakai, N.

1976-09-01

The problem of the Regge-cut cancellation in equations for planar Reggeons is considered by using the j-plane methods in treating the underlying integral equations. It is shown that the kernel should have the zero which cancels the Reggeon-loop singularity in order to eliminate the cut in the Reggeon-Reggeon scattering amplitudes besides amplitudes involving external particles. This zero (nonsense zero) implies that the finite size cluster is incompatable with the cut cancellation. Two alternatives no-double-counting conditions of the 'Reggeon-bootstrap' (the Oxford Rutherford model and the Finkelstein-Koplik model) are examined and it is found that the Regge-cut cannot be cancelled because of the finite size of the cluster. Substantial modifications of the 'Reggeon-bootstrap' model may be necessary if the Regge-cut is to be cancelled. (author)

Capsule calculus

CERN Document Server

Ritow, Ira

2003-01-01

This brief introductory text presents the basic principles of calculus from the engineering viewpoint. Excellent either as a refresher or as an introductory course, it focuses on developing familiarity with the basic principles rather than presenting detailed proofs.Topics include differential calculus, in terms of differentiation and elementary differential equations; integral calculus, in simple and multiple integration forms; time calculus; equations of motion and their solution; complex variables; complex algebra; complex functions; complex and operational calculus; and simple and inverse

Assuming Regge trajectories in holographic QCD: from OPE to Chiral Perturbation Theory

CERN Document Server

Cappiello, Luigi; Greynat, David

2015-01-01

The Soft Wall model in holographic QCD has Regge trajectories but wrong operator product expansion (OPE) for the two-point vectorial QCD Green function. We correct analytically this problem and describe the axial sector and chiral symmetry breaking. The low energy chiral parameters, $F_{\\pi}$ and $L_{10}$ , are well described analytically by the model in terms of Regge spacing and QCD condensates. The model nicely supports and extends previous theoretical analyses advocating Digamma function to study QCD two-point functions in different momentum regions.

Regge expansion of a casual spectral function in electroproduction

International Nuclear Information System (INIS)

Ahmed, M.A.; Taha, M.O.

1975-01-01

The conjecture that a term in the Regge espansion of the Deser-Gilbert-Sudarshan spectral function in electroproduction may identically vanish is investigated. It is shown that this conjecture does not appear to be in agreement with experiment

Calculus light

CERN Document Server

Friedman, Menahem

2011-01-01

Another Calculus book? As long as students find calculus scary, the failure rate in mathematics is higher than in all other subjects, and as long as most people mistakenly believe that only geniuses can learn and understand mathematics, there will always be room for a new book of Calculus. We call it Calculus Light. This book is designed for a one semester course in ""light"" calculus -- mostly single variable, meant to be used by undergraduate students without a wide mathematical background and who do not major in mathematics but study subjects such as engineering, biology or management infor

The (ℎ/2π)-expansion for Regge-trajectories. 2. Relativistic equations

International Nuclear Information System (INIS)

Stepanov, S.S.; Tutik, R.S.

1992-01-01

The (h/2π)-expansion method, proposed earlier for deriving Regge trajectories for bound states of central potentials in the Schroedinger equation framework, is extended to the Klein-Gordon and Dirac equations with potentials having vector and scalar components. The simple recursion formulae, with the same form both for the parent and daughter Regge trajectories, are obtained. They provide, in principle, the calculation of the (h/2π)-expansion terms up to an arbitrary order. As an illustration, a superposition of the vector and scalar Coulomb potentials, and the funnel-shaped potential are treated with the technique developed. 20 refs.; 3 figs.; 1 table. (author)

Geometry of lattice field theory

International Nuclear Information System (INIS)

Honan, T.J.

1986-01-01

Using some tools of algebraic topology, a general formalism for lattice field theory is presented. The lattice is taken to be a simplicial complex that is also a manifold and is referred to as a simplicial manifold. The fields on this lattice are cochains, that are called lattice forms to emphasize the connections with differential forms in the continuum. This connection provides a new bridge between lattice and continuum field theory. A metric can be put onto this simplicial manifold by assigning lengths to every link or I-simplex of the lattice. Regge calculus is a way of defining general relativity on this lattice. A geometric discussion of Regge calculus is presented. The Regge action, which is a discrete form of the Hilbert action, is derived from the Hilbert action using distribution valued forms. This is a new derivation that emphasizes the underlying geometry. Kramers-Wannier duality in statistical mechanics is discussed in this general setting. Nonlinear field theories, which include gauge theories and nonlinear sigma models are discussed in the continuum and then are put onto a lattice. The main new result here is the generalization to curved spacetime, which consists of making the theory compatible with Regge calculus

Calculus

CERN Document Server

Larson, Ron

2014-01-01

The Larson CALCULUS program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.

The role of leading twist operators in the Regge and Lorentzian OPE limits

Energy Technology Data Exchange (ETDEWEB)

Costa, Miguel S. [Centro de Física do Porto, Departamento de Física e Astronomia,Faculdade de Ciências da Universidade do Porto,Rua do Campo Alegre 687, 4169-007 Porto (Portugal); Drummond, James [CERN,Geneva 23 (Switzerland); School of Physics and Astronomy, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom); LAPTH, CNRS et Université de Savoie,F-74941 Annecy-le-Vieux Cedex (France); Gonçalves, Vasco; Penedones, João [Centro de Física do Porto, Departamento de Física e Astronomia,Faculdade de Ciências da Universidade do Porto,Rua do Campo Alegre 687, 4169-007 Porto (Portugal)

2014-04-14

We study two kinematical limits, the Regge limit and the Lorentzian OPE limit, of the four-point function of the stress-tensor multiplet in Super Yang-Mills at weak coupling. We explain how both kinematical limits are controlled by the leading twist operators. We use the known expression of the four-point function up to three loops, to extract the pomeron residue at next-to-leading order. Using this data and the known form of pomeron spin up to next-to-leading order, we predict the behaviour of the four-point function in the Regge limit at higher loops. Specifically, we determine the leading log behaviour at any loop order and the next-to-leading log at four loops. Finally, we check the consistency of our results with conformal Regge theory. This leads us to predict the behaviour around J=1 of the OPE coefficient of the spin J leading twist operator in the OPE of two chiral primary operators.

Solving QCD via multi-Regge theory

International Nuclear Information System (INIS)

White, A. R.

1998-01-01

To solve QCD at high-energy the authors must simultaneously find the hadronic states and the exchanged pomeron (IP) giving UNITARY scattering amplitudes. Experimentally, the IP ∼ a Regge pole at small Q 2 and a single gluon at larger Q 2 . (F 2 D -H1, dijets-ZEUS). In the solution which the author describes, these non-perturbative properties of the IP are directly related to the non-perturbative confinement and chiral symmetry breaking properties of hadrons

Continuation calculus

NARCIS (Netherlands)

Geron, B.; Geuvers, J.H.; de'Liguoro, U.; Saurin, A.

2013-01-01

Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic model of computation that is evaluated using only head

Collinear and Regge behavior of 2{yields}4 MHV amplitude in N=4 super Yang-Mills theory

Energy Technology Data Exchange (ETDEWEB)

Bartels, J.; Prygarin, A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; St. Petersburg Nuclear Physics Institute (Russian Federation)

2011-04-15

We investigate the collinear and Regge behavior of the 2{yields}4 MHV amplitude in N=4 super Yang-Mills theory in the BFKL approach. The expression for the remainder function in the collinear kinematics proposed by Alday, Gaiotto, Maldacena, Sever and Vieira is analytically continued to the Mandelstam region. The result of the continuation in the Regge kinematics shows an agreement with the BFKL approach up to to five-loop level. We present the Regge theory interpretation of the obtained results and discuss some issues related to a possible nonmultiplicative renormalization of the remainder function in the collinear limit. (orig.)

Impact of Calculus Reform in a Liberal Arts Calculus Course.

Science.gov (United States)

Brosnan, Patricia A.; Ralley, Thomas G.

This report describes the changes in a freshman-level calculus course that occurred as a consequence of adopting the Harvard Consortium Calculus text. The perspective is that of the lecturer. The course is intended as an introduction to calculus for liberal arts students, that is, students who will not be expected to use calculus as a mathematical…

Discrete quantum gravity

International Nuclear Information System (INIS)

Williams, J.W.

1992-01-01

After a brief introduction to Regge calculus, some examples of its application is quantum gravity are described in this paper. In particular, the earliest such application, by Ponzano and Regge, is discussed in some detail and it is shown how this leads naturally to current work on invariants of three-manifolds

High energy behaviour of nonabelian gauge theories

International Nuclear Information System (INIS)

Bartels, J.

1979-10-01

The high energy behavior (in the Regge limit) of nonabelian gauge theories is reviewed. After a general remark concerning the question to what extent the Regge limit can be approached within perturbation theory, we first review the reggeization of elementary particles within nonabelian gauge theories. Then the derivation of a unitary high energy description of a massive (= spontaneously broken) nonabelian gauge model is described, which results in a complete reggeon calculus. There is strong evidence that the zero mass limit of this reggeon calculus exists, thus giving rise to the hope that the Regge behavior in pure Yang-Mills theories (QCD) can be reached in this way. In the final part of these lectures two possible strategies for solving this reggeon calculus (both for the massive and the massless case) are outlined. One of them leads to a geometrical picture in which the distribution of the wee partons obeys a diffusion law. The other one makes contact with reggeon field theory and predicts that QCD in the high energy limit is described by critical reggeon field theory. (orig.)

Calculus

CERN Document Server

Grossman, Stanley I

1981-01-01

Calculus, Second Edition discusses the techniques and theorems of calculus. This edition introduces the sine and cosine functions, distributes ?-? material over several chapters, and includes a detailed account of analytic geometry and vector analysis.This book also discusses the equation of a straight line, trigonometric limit, derivative of a power function, mean value theorem, and fundamental theorems of calculus. The exponential and logarithmic functions, inverse trigonometric functions, linear and quadratic denominators, and centroid of a plane region are likewise elaborated. Other topics

Pomeron models and exchange degeneracy of the Regge trajectories

International Nuclear Information System (INIS)

Kontros, J.; Kontros, K.; Lengyel, A.

2000-01-01

Two models for the Pomeron, supplemented by exchange-degenerate sub-leading Regge trajectories, are fitted to the forward scattering data for a number of reactions. By considering new Pomeron models, we extend the recent results of the COMPAS group, being consistent with our predecessors

Operational calculus

CERN Document Server

Boehme, Thomas K

1987-01-01

Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included.Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and non-ho

Solving QCD using multi-regge theory

International Nuclear Information System (INIS)

White, A. R.

1998-01-01

This talk outlines the derivation of a high-energy, transverse momentum cut-off, solution of QCD in which the Regge pole and ''single gluon'' properties of the pomeron are directly related to the confinement and chiral symmetry breaking properties of the hadron spectrum. In first approximation, the pomeron is a single reggeized gluon plus a ''wee parton'' component that compensates for the color and particle properties of the gluon. This solution corresponds to a supercritical phase of Reggeon Field Theory

Fundamentals of calculus

CERN Document Server

Morris, Carla C

2015-01-01

Fundamentals of Calculus encourages students to use power, quotient, and product rules for solutions as well as stresses the importance of modeling skills.  In addition to core integral and differential calculus coverage, the book features finite calculus, which lends itself to modeling and spreadsheets.  Specifically, finite calculus is applied to marginal economic analysis, finance, growth, and decay.  Includes: Linear Equations and FunctionsThe DerivativeUsing the Derivative Exponential and Logarithmic Functions Techniques of DifferentiationIntegral CalculusIntegration TechniquesFunctions

Ponzano-Regge model revisited: I. Gauge fixing, observables and interacting spinning particles

International Nuclear Information System (INIS)

Freidel, Laurent; Louapre, David

2004-01-01

We show how to properly gauge fix all the symmetries of the Ponzano-Regge model for 3D quantum gravity. This amounts to doing explicit finite computations for transition amplitudes. We give the construction of the transition amplitudes in the presence of interacting quantum spinning particles. We introduce a notion of operators whose expectation value gives rise to either gauge fixing, introduction of time, or insertion of particles, according to the choice. We give the link between the spin foam quantization and the Hamiltonian quantization. We finally show the link between the Ponzano-Regge model and the quantization of Chern-Simons theory based on the double quantum group of SU(2)

Regge calculus in teleparallel gravity

International Nuclear Information System (INIS)

Pereira, J G; Vargas, T

2002-01-01

In the context of the teleparallel equivalent of general relativity, the Weitzenboeck manifold is considered as the limit of a suitable sequence of discrete lattices composed of an increasing number of smaller and smaller simplices, where the interior of each simplex (Delaunay lattice) is assumed to be flat. The link lengths l between any pair of vertices serve as independent variables, so that torsion turns out to be localized in the two-dimensional hypersurfaces (dislocation triangle, or hinge) of the lattice. Assuming that a vector undergoes a dislocation in relation to its initial position as it is parallel transported along the perimeter of the dual lattice (Voronoi polygon), we obtain the discrete analogue of the teleparallel action, as well as the corresponding simplicial vacuum field equations

Calculus refresher

CERN Document Server

Klaf, A A

1956-01-01

This book is unique in English as a refresher for engineers, technicians, and students who either wish to brush up their calculus or find parts of calculus unclear. It is not an ordinary textbook. It is, instead, an examination of the most important aspects of integral and differential calculus in terms of the 756 questions most likely to occur to the technical reader. It provides a very easily followed presentation and may also be used as either an introductory or supplementary textbook. The first part of this book covers simple differential calculus, with constants, variables, functions, inc

Regge cuts in inclusive reactions

International Nuclear Information System (INIS)

Paige, F.E.; Trueman, T.L.

1975-01-01

The contribution of Regge cuts to single-particle inclusive processes is analyzed using the techniques of Gribov. The dependence of these contributions on the polarization state of the target is emphasized. A general formula is obtained and certain contributions to it are calculated. It is not possible, however, to reduce this to a simple, powerful formula expressing the total cut contribution in terms of other measurable quantities, as can be done for the cut contribution to the total cross section. The reasons for this are discussed in detail. The single-particle intermediate states, analogous to the absorption model for elastic scattering, are explicitly calculated as an illustration

Simplicial lattices in classical and quantum gravity: Mathematical structure and application

International Nuclear Information System (INIS)

LaFave, N.J.

1989-01-01

Geometrodynamics can be understood more clearly in the language of geometry than in the language of differential equations. This is the primary motivation for the development of calculational schemes based on Regge Calculus as an alternative to those schemes based on Ricci Calculus. The author develops the mathematics of simplicial lattices to the same level of sophistication as the mathematics of pseudo-Riemannian geometry for continuum manifolds. This involves the definition of the simplicial analogues of several concepts from differential topology and differential geometry-the concept of a point, tangent spaces, forms, tensors, parallel transport, covariant derivatives, connections, and curvature. These simplicial analogues are used to define the Einstein tensor and the extrinsic curvature on a simplicial geometry. He applies this mathematical formalism to the solution of several outstanding problems in the development of a Regge Calculus based computational scheme for general geometrodynamic problems. This scheme is based on a 3 + 1 splitting of spacetime within the Regge Calculus prescription known as Null-Strut Calculus (NSC). NSC, developed by Warner Miller, describes the foliation of spacetime into spacelike hypersurfaces built of tetrahedra. The outstanding problems discussed include (a) the rigidification of the 3-layered sandwich and the evolution problem; (b) the formulation of initial data; and (c) in inclusion of matter on the lattice. The resulting calculational scheme is applied to two test problems, the Friedmann model and the second-order Doppler effect. Finally, he describes avenues of investigation for NSC in quantum gravity

Vector Differential Calculus

OpenAIRE

HITZER, Eckhard MS

2002-01-01

This paper treats the fundamentals of the vector differential calculus part of universal geometric calculus. Geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. In order to make the treatment self-contained, I first compile all important geometric algebra relationships,which are necesssary for vector differential calculus. Then differentiation by vectors is introduced and a host of major ve...

Simple Regge pole model for Compton scattering of protons

International Nuclear Information System (INIS)

Saleem, M.; Fazal-e-Aleem

1978-01-01

It is shown that by a phenomenological choice of the residue functions, the differential cross section for ν p → ν p, including the very recent measurements up to - t=4.3 (GeV/c) 2 , can be explained at all measured energies greater than 2 GeV with simple Regge pole model

The impact of taking a college pre-calculus course on students' college calculus performance

Science.gov (United States)

Sonnert, Gerhard; Sadler, Philip M.

2014-11-01

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and four-year colleges continues to grow, and these courses are well-populated with students who already took pre-calculus in high school. We examine student performance in college calculus, using regression discontinuity to estimate the effects of taking college pre-calculus or not, in a national US sample of 5507 students at 132 institutions. We find that students who take college pre-calculus do not earn higher calculus grades.

Study on bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis.

Science.gov (United States)

Wan, Tien-Chun; Cheng, Fu-Yuan; Liu, Yu-Tse; Lin, Liang-Chuan; Sakata, Ryoichi

2009-12-01

The purpose of the study was to investigate bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis obtained as valuable by-products from animals used for meat production. The results showed that the components of natural Calculus Bovis were rich in bilirubin and biliverdin and had higher content of essential amino acids. The major amino acids of in vitro cultured Calculus Suis were identified as glycine, alanine, glutamic acid and aspartic acid, and those for natural Calculus Bovis were found to be glutamic acid, aspartic acid, proline, and arginine. The methionine and cysteine contents of precursors for glutathione in natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The mineral contents of zinc, iron and manganese of natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The major bile acids in both products were cholic acid and dehydrocholic acid, respectively. The chenodeoxycholic and ursodeoxycholic acid content of in vitro cultured Calculus Suis was significantly higher than that of natural Calculus Bovis.

Models of Regge behaviour in an asymptotically free theory

International Nuclear Information System (INIS)

Polkinghorne, J.C.

1976-01-01

Two simple Feynman integral models are presented which reproduce the features expected to be of physical importance in the Regge behaviour of asymptotically free theories. Analysis confirms the result, expected on general grounds, that phi 3 in six dimensions has an essential singularity at l=-1. The extension to gauge theories is discussed. (Auth.)

Propositional Calculus in Coq

OpenAIRE

van Doorn, Floris

2015-01-01

I formalize important theorems about classical propositional logic in the proof assistant Coq. The main theorems I prove are (1) the soundness and completeness of natural deduction calculus, (2) the equivalence between natural deduction calculus, Hilbert systems and sequent calculus and (3) cut elimination for sequent calculus.

Regge parametrization of angular distributions for heavy-ion transfer reactions

International Nuclear Information System (INIS)

Carlson, B.V.; McVoy, K.W.

1977-01-01

A two-pole one-zero Regge parametrization of the l-window for transfer reactions is employed in conjunction with a chi-squared search program to obtain high-quality fits to a wide variety of transfer data. The data employed include both direct and multi-step transfers. (Auth.)

Extraction of Structure Function and Gluon Distribution Function at Low-x from Cross Section Derivative by Regge Behavior

International Nuclear Information System (INIS)

Boroun, G.R.

2005-01-01

An approximation method based on Regge behavior is presented. This new method relates the reduced cross section derivative and the structure function Regge behavior at low x. With the use of this approximation method, the C and λ parameters are calculated from the HERA reduced cross section data taken at low-x. Also, we calculate the structure functions F 2 (x,Q 2 ) even for low-x values, which have not been investigated. To test the validity of calculated structure functions, we find the gluon distribution function in the Leading order approximation based on Regge behaviour of structure function and compare to the NLO QCD fit to H1 data and NLO parton distribution function.

Tuplix Calculus

OpenAIRE

Bergstra, J. A.; Ponse, A.; van der Zwaag, M. B.

2007-01-01

We introduce a calculus for tuplices, which are expressions that generalize matrices and vectors. Tuplices have an underlying data type for quantities that are taken from a zero-totalized field. We start with the core tuplix calculus CTC for entries and tests, which are combined using conjunctive composition. We define a standard model and prove that CTC is relatively complete with respect to it. The core calculus is extended with operators for choice, information hiding, scalar multiplicatio...

Noncausal stochastic calculus

CERN Document Server

Ogawa, Shigeyoshi

2017-01-01

This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but ...

Quark contribution to the gluon Regge trajectory at NLO from the high energy effective action

International Nuclear Information System (INIS)

Chachamis, G.; Hentschinski, M.; Madrigal Martínez, J.D.; Sabio Vera, A.

2012-01-01

The two loop (NLO) diagrams with quark content contributing to the gluon Regge trajectory are computed within the framework of Lipatov's effective action for QCD, using the regularization procedure for longitudinal divergencies recently proposed by two of us in (M. Hentschinski and A. Sabio Vera, 2011). Perfect agreement with previous results in the literature is found, providing a robust check of the regularization prescription and showing that the high energy effective action is a very useful computational tool in the quasi-multi-Regge limit.

Continuation calculus

Directory of Open Access Journals (Sweden)

Bram Geron

2013-09-01

Full Text Available Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic model of computation that is evaluated using only head reduction, and argue that it is suitable for modeling programs with control. It is demonstrated how to define programs, specify them, and prove them correct. This is shown in detail by presenting in CC a list multiplication program that prematurely returns when it encounters a zero. The correctness proof includes termination of the program. In continuation calculus we can model both call-by-name and call-by-value. In addition, call-by-name functions can be applied to call-by-value results, and conversely.

Dimensional reduction and BRST approach to the description of a Regge trajectory

International Nuclear Information System (INIS)

Pashnev, A.I.; Tsulaya, M.M.

1997-01-01

The local free field theory for Regge trajectory is described in the framework of the BRST-quantization method. The corresponding BRST-charge is constructed with the help of the method of dimensional reduction

Minimal Regge model for meson--baryon scattering: duality, SU(3) and phase-modified absorptive cuts

International Nuclear Information System (INIS)

Egli, S.E.

1975-10-01

A model is presented which incorporates economically all of the modifications to simple SU(3)-symmetric dual Regge pole theory which are required by existing data on 0 -1 / 2 + → -1 / 2 + processes. The basic assumptions are no-exotics duality, minimally broken SU(3) symmetry, and absorptive Regge cuts phase-modified by the Ringland prescription. First it is described qualitatively how these assumptions suffice for the description of all measured reactions, and then the results of a detailed fit to 1987 data points are presented for 18 different reactions. (auth)

Calculus II For Dummies

CERN Document Server

Zegarelli, Mark

2012-01-01

An easy-to-understand primer on advanced calculus topics Calculus II is a prerequisite for many popular college majors, including pre-med, engineering, and physics. Calculus II For Dummies offers expert instruction, advice, and tips to help second semester calculus students get a handle on the subject and ace their exams. It covers intermediate calculus topics in plain English, featuring in-depth coverage of integration, including substitution, integration techniques and when to use them, approximate integration, and improper integrals. This hands-on guide also covers sequences and series, wit

Infra-red divergences and Regge behaviour in QCD

International Nuclear Information System (INIS)

Jaroszewicz, T.

1980-01-01

We analyze high energy behaviour of multi-gluon exchange amplitudes in the leading-lns approximation in perturbation theory. Working in the Coulomb gauge and employing Ward identities we derive an integral equation for the n-gluon system in the exchange channel. We find that the Regge behaviour is associated with exponentiation of leading infrared divergences, and the position of the j-plane singularities is determined by the colour quantum numbers of the exchanged system. (author)

Early Vector Calculus: A Path through Multivariable Calculus

Science.gov (United States)

Robertson, Robert L.

2013-01-01

The divergence theorem, Stokes' theorem, and Green's theorem appear near the end of calculus texts. These are important results, but many instructors struggle to reach them. We describe a pathway through a standard calculus text that allows instructors to emphasize these theorems. (Contains 2 figures.)

Multi-Regge amplitudes for bremsstrahlung in e+e- backward scattering

International Nuclear Information System (INIS)

Ermolaev, B.I.; Lipatov, L.N.

1988-01-01

Using the method of factorization, equations are obtained for the inelastic on-shell amplitudes describing the asymptotic behavior of e + e - backward scattering with emission of bremsstrahlung photons in the doubly logarithmic approximation. Explicit expressions are found for these amplitudes in the case in which the photons are emitted with multi-Regge kinematics

Calculus

CERN Document Server

Spivak, Michael

2006-01-01

Spivak's celebrated textbook is widely held as one of the finest introductions to mathematical analysis. His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

Regge behaviour of structure functions and evolution of gluon structure function upto next-to-leading order at low-x

International Nuclear Information System (INIS)

Jamil, U.; Sarma, J.K.

2011-01-01

Evolution of gluon structure function from Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations upto next-to-leading order at low-x is presented assuming the Regge behaviour of structure functions. We compare our results of gluon structure function with GRV 98 global parameterization and show the compatibility of Regge behaviour of structure functions with PQCD. (author)

Gravity-matter entanglement in Regge quantum gravity

International Nuclear Information System (INIS)

Paunković, Nikola; Vojinović, Marko

2016-01-01

We argue that Hartle-Hawking states in the Regge quantum gravity model generically contain non-trivial entanglement between gravity and matter fields. Generic impossibility to talk about “matter in a point of space” is in line with the idea of an emergent spacetime, and as such could be taken as a possible candidate for a criterion for a plausible theory of quantum gravity. Finally, this new entanglement could be seen as an additional “effective interaction”, which could possibly bring corrections to the weak equivalence principle. (paper)

Regge in the sky: Origin of the cosmic rotation

International Nuclear Information System (INIS)

Muradian, R.

1994-06-01

Observed universal spin and mass relationship for a wide range of astronomical objects are described by two extended Regge trajectories: disc-trajectory for stars and planets, and ball-trajectory for galaxies and their clusters. The cosmic Chew-Frautschi plot is presented and two fundamental points are revealed on it: Eddington and Chandrasekhar points with coordinates expressed via combinations of the fundamental constants. (author). 17 refs, 3 figs

The non-ordinary Regge behavior of the K{sup *}{sub 0}(800) or κ-meson versus the ordinary K{sup *}{sub 0}(1430)

Energy Technology Data Exchange (ETDEWEB)

Pelaez, J.R.; Rodas, A. [Universidad Complutense de Madrid, Departamento de Fisica Teorica II and UPARCOS, Madrid (Spain)

2017-06-15

The Regge trajectory of an elastic resonance can be calculated from dispersion theory, instead of fitted phenomenologically, using only its pole parameters as input. This also provides a correct treatment of resonance widths in Regge trajectories, essential for very wide resonances. In this work we first calculate the K{sup *}{sub 0}(1430) Regge trajectory, finding the ordinary almost real and linear behavior, typical of q anti q resonances. In contrast, for the K{sup *}{sub 0}(800) meson, the resulting Regge trajectory is non-linear and has a much smaller slope than ordinary resonances, being remarkably similar to that of the f{sub 0}(500) or σ meson. The slope of these unusual Regge trajectories seems to scale with the meson masses rather than with scales typical of quark degrees of freedom. We also calculate the range of the interaction responsible for the formation of these resonances. Our results strongly support a non-ordinary, predominantly meson-meson-like, interpretation for the lightest strange and non-strange resonances. (orig.)

Tuplix calculus

NARCIS (Netherlands)

Bergstra, J.A.; Ponse, A.; van der Zwaag, M.B.

2008-01-01

We introduce a calculus for tuplices, which are expressions that generalize matrices and vectors. Tuplices have an underlying data type for quantities that are taken from a zero-totalized field. We start with the core tuplix calculus CTC for entries and tests, which are combined using conjunctive

Patterns of High energy Massive String Scatterings in the Regge Regime

International Nuclear Information System (INIS)

Lee Jen Chi

2009-01-01

We calculate high energy massive string scattering amplitudes of open bosonic string in the Regge regime (RR). We found that the number of high energy amplitudes for each fixed mass level in the RR is much more numerous than that of Gross regime (GR) calculated previously. Moreover, we discover that the leading order amplitudes in the RR can be expressed in terms of the Kummer function of the second kind. In particular, based on a summation algorithm for Stirling number identities developed recently, we discover that the ratios calculated previously among scattering amplitudes in the GR can be extracted from this Kummer function in the RR. We conjecture and give evidences that the existence of these GR ratios in the RR persists to sub-leading orders in the Regge expansion of all string scattering amplitudes. Finally, we demonstrate the universal power-law behavior for all massive string scattering amplitudes in the RR. (author)

Calculus with applications

CERN Document Server

Lax, Peter D

2014-01-01

This new edition of Lax, Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physical sciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings the innovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of  functions, uniform convergence is more natural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers and complex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an introduc...

Discrete fractional calculus

CERN Document Server

Goodrich, Christopher

2015-01-01

This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...

On the Regge-Wheeler Tortoise and the Kruskal-Szekeres Coordinates

Directory of Open Access Journals (Sweden)

Crothers S. J.

2006-07-01

Full Text Available The Regge-Wheeler tortoise “coordinate” and the the Kruskal-Szekeres “extension” are built upon a latent set of invalid assumptions. Consequently, they have led to fallacious conclusions about Einstein’s gravitational field. The persistent unjustified claims made for the aforesaid alleged coordinates are not sustained by mathematical rigour. They must therefore be discarded.

Regge-like initial input and evolution of non-singlet structure ...

Indian Academy of Sciences (India)

Regge-like initial input and evolution of non-singlet structure functions from DGLAP equation up to next-next-to-leading order at low x and low Q. 2. NAYAN MANI NATH1,2,∗, MRINAL KUMAR DAS1 and JAYANTA KUMAR SARMA1. 1Department of Physics, Tezpur University, Tezpur 784 028, India. 2Department of Physics ...

Regge limit of R-current correlators in AdS supergravity

International Nuclear Information System (INIS)

Bartels, J.; Kotanski, J.; Mischler, A.M.; Schomerus, V.

2009-08-01

Four-point functions of R-currents are discussed within Anti-de Sitter supergravity. In particular, we compute Witten diagrams with graviton and gauge boson exchange in the high energy Regge limit. Assuming validity of the AdS/CFT correspondence, our results apply to R-current four-point functions of N=4 super Yang-Mills theory at strong coupling. (orig.)

Calculus of one variable

CERN Document Server

Grossman, Stanley I

1986-01-01

Calculus of One Variable, Second Edition presents the essential topics in the study of the techniques and theorems of calculus.The book provides a comprehensive introduction to calculus. It contains examples, exercises, the history and development of calculus, and various applications. Some of the topics discussed in the text include the concept of limits, one-variable theory, the derivatives of all six trigonometric functions, exponential and logarithmic functions, and infinite series.This textbook is intended for use by college students.

Time scales: from Nabla calculus to Delta calculus and vice versa via duality

OpenAIRE

Caputo, M. Cristina

2009-01-01

In this note we show how one can obtain results from the nabla calculus from results on the delta calculus and vice versa via a duality argument. We provide applications of the main results to the calculus of variations on time scales.

The calculus lifesaver all the tools you need to excel at calculus

CERN Document Server

Banner, Adrian

2009-01-01

For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it. All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of

On the refinement calculus

CERN Document Server

Vickers, Trevor

1992-01-01

On the Refinement Calculus gives one view of the development of the refinement calculus and its attempt to bring together - among other things - Z specifications and Dijkstra's programming language. It is an excellent source of reference material for all those seeking the background and mathematical underpinnings of the refinement calculus.

Unitarization of pomeron and Regge phenomenology of deep inelastic scattering.

Energy Technology Data Exchange (ETDEWEB)

Martynov, E S

1994-12-31

Using conventional Regge approach we consider unitarization of supercritical pomeron in DIS and then describe the total photon-proton cross-section and the proton structure functions in the region W{sup 2} = Q{sup 2}(1/x-1) + m{sup 2} {>=} 9 GeV{sup 2}, including the small-x data from HERA. (author). 15 refs., 1 tab., 15 figs.

The Impact of Taking a College Pre-Calculus Course on Students' College Calculus Performance

Science.gov (United States)

Sonnert, Gerhard; Sadler, Philip M.

2014-01-01

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and…

Applying π-Calculus to Practice

DEFF Research Database (Denmark)

Abendroth, Jorg

2003-01-01

The π-Calculus has been developed to reason about behavioural equivalence. Different notations of equivalence are defined in terms of process interactions, as well as the context of processes. There are various extensions of the π-Calculus, such as the SPI calculus, which has primitives...... modles are instantiated correctly. In this paper we will utilize the to π-Calculus reason about access control policies and mechanism. An equivalence of different policy implementations, as well as access control mechanism will be shown. Finally some experiences regarding the use of π-Calculus...

Regge behaviour and Bjorken scaling for deep-inelastic lepton-hadron scattering process

International Nuclear Information System (INIS)

Tran Huu Phat

1976-01-01

Within the framework of the Jost-Lehmann-Dyson (JLD) representation and the renormalization-group (RG) equation, it is shown that either the RG technique is not applicable to deep-inelastic phenomena or Regge behaviour and Bjorken scaling for structure functions do not coexist. (author)

A generalized nonlocal vector calculus

Science.gov (United States)

Alali, Bacim; Liu, Kuo; Gunzburger, Max

2015-10-01

A nonlocal vector calculus was introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A formulation is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal integration by parts formula and Green's identities. The nonlocal vector calculus introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) is shown to be recoverable from the general formulation as a special example. This special nonlocal vector calculus is used to reformulate the peridynamics equation of motion in terms of the nonlocal gradient operator and its adjoint. A new example of nonlocal vector calculus operators is introduced, which shows the potential use of the general formulation for general nonlocal models.

Four point function of R-currents in N=4 SYM in the Regge limit at weak coupling

Energy Technology Data Exchange (ETDEWEB)

Bartels, J.; Mischler, A.M.; Salvadore, M. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

2008-04-15

We compute, in N = 4 super Yang-Mills, the four point correlation function of R-currents in the Regge limit in the leading logarithmic approximation at weak coupling. Such a correlator is the closest analog to photon-photon scattering within QCD, and there is a well defined procedure to perform the analogous computation at strong coupling via AdS/CFT. The main result of this paper is, on the gauge theory side, the proof of Regge factorization and the explicit computation of the R-current impact factors. (orig.)

Multivariable calculus with applications

CERN Document Server

Lax, Peter D

2017-01-01

This text in multivariable calculus fosters comprehension through meaningful explanations. Written with students in mathematics, the physical sciences, and engineering in mind, it extends concepts from single variable calculus such as derivative, integral, and important theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems. Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathemat...

Calculus

CERN Document Server

Grossman, Stanley I

1984-01-01

Calculus, Third Edition emphasizes the techniques and theorems of calculus, including many applied examples and exercises in both drill and applied-type problems.This book discusses shifting the graphs of functions, derivative as a rate of change, derivative of a power function, and theory of maxima and minima. The area between two curves, differential equations of exponential growth and decay, inverse hyperbolic functions, and integration of rational functions are also elaborated. This text likewise covers the fluid pressure, ellipse and translation of axes, graphing in polar coordinates, pro

Calculus of variations

CERN Document Server

Elsgolc, L E; Stark, M

1961-01-01

Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency

Analysis of pp scattering at the CERN ISR energies in the multiple Regge pole model

International Nuclear Information System (INIS)

Bugrij, A.I.; Kobylinsky, N.A.

1976-01-01

The simple Regge model is suggested for describing data on proton-proton elastic scattering at high energies. The simplest variant of the Regge model can be formulated as a sum of two pomerons, the first being a moving double pole and the second - a fixed simple pole. Comparison with known data is given. The model gives an infinite rise of the total cross section of pp-scattering. The differential cross section changes slowly with energy. The models of two pomerons reproduce many features of the geometric scaling, in particular, the shift of the dip and rise of scattering total cross section at the second maximum. The considered model is rather simple and is well consistent with experiment

Structure and properties of Regge-Mueller diagrams for the case of Froissart saturation

International Nuclear Information System (INIS)

Kobylinsky, N.A.; Kosenko, A.I.; Martynov, E.S.

1976-01-01

A model leading to the Froissart saturation in various diffractive and nondiffractive production processes is elaborated. The restrictions on a structure of Regge-Mueller diagrams are obtained in the model. A comparison is made of the pomeron, dipole and froissaron models

Polynomial Calculus: Rethinking the Role of Calculus in High Schools

Science.gov (United States)

Grant, Melva R.; Crombie, William; Enderson, Mary; Cobb, Nell

2016-01-01

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…

Calculus for dummies

CERN Document Server

Ryan, Mark

2014-01-01

Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable-even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the ""how"" and ""why"" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll s

Advanced calculus a transition to analysis

CERN Document Server

Dence, Thomas P

2010-01-01

Designed for a one-semester advanced calculus course, Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis -- providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. Ancillary list: * Companion website, Ebook- http://www.elsevierdirect.com/product.jsp?isbn=9780123749550 * Student Solutions Manual- To come * Instructor

Maxima and Minima Without Calculus.

Science.gov (United States)

Birnbaum, Ian

1982-01-01

Approaches to extrema that do not require calculus are presented to help free maxima/minima problems from the confines of calculus. Many students falsely suppose that these types of problems can only be dealt with through calculus, since few, if any, noncalculus examples are usually presented. (MP)

The quantum probability calculus

International Nuclear Information System (INIS)

Jauch, J.M.

1976-01-01

The Wigner anomaly (1932) for the joint distribution of noncompatible observables is an indication that the classical probability calculus is not applicable for quantum probabilities. It should, therefore, be replaced by another, more general calculus, which is specifically adapted to quantal systems. In this article this calculus is exhibited and its mathematical axioms and the definitions of the basic concepts such as probability field, random variable, and expectation values are given. (B.R.H)

Paragrassmann differential calculus

International Nuclear Information System (INIS)

Filippov, A.T.; Isaev, A.P.; Kurdikov, A.V.

1993-01-01

This paper significantly extends and generalizes the paragrassmann calculus previous paper. Explicit general constructions for paragrassmann calculus with one and many vaiables are discussed. A general construction of many-variable differentiation algebras is given. Some particular examples are related to multi-parametric quantum deformation of the harmonic oscillators

The efficacy of selective calculus ablation at 400 nm: comparison to conventional calculus removal methods

Science.gov (United States)

Schoenly, Joshua E.; Seka, Wolf; Romanos, Georgios; Rechmann, Peter

A desired outcome of scaling and root planing is the complete removal of calculus and infected root tissue and preservation of healthy cementum for rapid healing of periodontal tissues. Conventional periodontal treatments for calculus removal, such as hand instrument scaling and ultrasonic scaling, often deeply scrape the surface of the underlying hard tissue and may leave behind a smear layer. Pulsed lasers emitting at violet wavelengths (specifically, 380 to 400 nm) are a potential alternative treatment since they can selectively ablate dental calculus without ablating pristine hard tissue (i.e., enamel, cementum, and dentin). In this study, light and scanning electron microscopy are used to compare and contrast the efficacy of in vitro calculus removal for several conventional periodontal treatments (hand instruments, ultrasonic scaler, and Er:YAG laser) to calculus removal with a frequency-doubled Ti:sapphire (λ = 400 nm). After calculus removal, enamel and cementum surfaces are investigated for calculus debris and damage to the underlying hard tissue surface. Compared to the smear layer, grooves, and unintentional hard tissue removal typically found using these conventional treatments, calculus removal using the 400-nm laser is complete and selective without any removal of pristine dental hard tissue. Based on these results, selective ablation from the 400-nm laser appears to produce a root surface that would be more suitable for successful healing of periodontal tissues.

Intercepts and residues of Regge poles in a stochastic-field multiparticle theory

International Nuclear Information System (INIS)

Arnold, R.C.

1976-01-01

A dynamical theory of multiparticle amplitudes, based on a functional integral representation embodying collective long-range correlations, is applied to the calculation of Regge intercepts and residues. Poles arising in conventional multiperipheral models will characteristically be modified in three ways: promotion, renormalization, and a proliferation of dynamical secondary trajectories, reminiscent of dual models

[Fluorescence control of dental calculus removal].

Science.gov (United States)

Bakhmutov, D N; Gonchukov, S A; Lonkina, T V; Sukhinina, A V

2012-01-01

The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In the frames of this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise detection of tooth-calculus interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing (as ultrasonic or laser devices).

A Logical Process Calculus

Science.gov (United States)

Cleaveland, Rance; Luettgen, Gerald; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

This paper presents the Logical Process Calculus (LPC), a formalism that supports heterogeneous system specifications containing both operational and declarative subspecifications. Syntactically, LPC extends Milner's Calculus of Communicating Systems with operators from the alternation-free linear-time mu-calculus (LT(mu)). Semantically, LPC is equipped with a behavioral preorder that generalizes Hennessy's and DeNicola's must-testing preorder as well as LT(mu's) satisfaction relation, while being compositional for all LPC operators. From a technical point of view, the new calculus is distinguished by the inclusion of: (1) both minimal and maximal fixed-point operators and (2) an unimple-mentability predicate on process terms, which tags inconsistent specifications. The utility of LPC is demonstrated by means of an example highlighting the benefits of heterogeneous system specification.

A Calculus for Context-Awareness

DEFF Research Database (Denmark)

Zimmer, Pascal

2005-01-01

In order to answer the challenge of pervasive computing, we propose a new process calculus, whose aim is to describe dynamic systems composed of agents able to move and react differently depending on their location. This Context-Aware Calculus features a hierarchical structure similar to mobile...... ambients, and a generic multi-agent synchronization mechanism, inspired from the join-calculus. After general ideas and introduction, we review the full calculus' syntax and semantics, as well as some motivating examples, study its expressiveness, and show how the notion of computation itself can be made...

Regge poles and Mandelstam representation in potential scattering; Poles de regge et representation de Mandelstam en theorie du potentiel

Energy Technology Data Exchange (ETDEWEB)

Bessis, D [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1965-03-01

We deal with the scattering of two spinless particles interacting by a superposition of Yukawa potentials. We first obtain an upper bound for the scattering amplitude for simultaneous complex values of energy and angular momentum. We then show that the Regge poles remain confined in small domains of the complex angular momentum plane, we study the variation of these domains when the energy (complex) varies. These first results allow us to deduce an upper bound for the double spectral function, this upper bound is used to rigorously show that the Schroedinger equation implies the Mandelstam representation for the type of potentials we deal with. Finally, the problem of subtractions is entirely solved, showing that the Mellin transform of the double spectral function can be analytically continued into the different simple spectral functions. (author) [French] On traite de la diffusion de deux particules sans spin interagissant par l'intermediaire d'une superposition de potentiels de Yukawa. Nous obtenons tout d'abord une majorante pour l'amplitude de diffusion pour des valeurs simultanement complexes de l'energie et du moment cinetique. On montre alors que les Poles de Regge restent confines dans des domaines restreints du plan complexe du moment cinetique, domaines dont nous etudions la variation pour des valeurs complexes de l'energie. Ces premiers resultats nous permettent alors de deduire une majorante pour la fonction spectrale double, majorante qui est utilisee pour demontrer rigoureusement que l'equation de Schroedinger implique la representation de Mandelstam pour la classe des potentiels envisages. Enfin le probleme des soustractions est entierement resolu, en montrant que la transformee de Mellin de la fonction spectrale double se prolonge analytiquement dans les diverses fonctions spectrales simples. (auteur)

Discrete gravity as a local theory of the Poincare group in the first-order formalism

Energy Technology Data Exchange (ETDEWEB)

Gionti, Gabriele [Vatican Observatory Research Group, Steward Observatory, 933 North Cherry Avenue, University of Arizona, Tucson, AZ 85721 (United States); Specola Vaticana, V-00120 Citta Del Vaticano (Vatican City State, Holy See,)

2005-10-21

A discrete theory of gravity, locally invariant under the Poincare group, is considered as in a companion paper. We define a first-order theory, in the sense of Palatini, on the metric-dual Voronoi complex of a simplicial complex. We follow the same spirit as the continuum theory of general relativity in the Cartan formalism. The field equations are carefully derived taking in account the constraints of the theory. They look very similar to first-order Einstein continuum equations in the Cartan formalism. It is shown that in the limit of small deficit angles these equations have Regge calculus, locally, as the only solution. A quantum measure is easily defined which does not suffer the ambiguities of Regge calculus, and a coupling with fermionic matter is easily introduced.

Discrete gravity as a local theory of the Poincare group in the first-order formalism

International Nuclear Information System (INIS)

Gionti, Gabriele

2005-01-01

A discrete theory of gravity, locally invariant under the Poincare group, is considered as in a companion paper. We define a first-order theory, in the sense of Palatini, on the metric-dual Voronoi complex of a simplicial complex. We follow the same spirit as the continuum theory of general relativity in the Cartan formalism. The field equations are carefully derived taking in account the constraints of the theory. They look very similar to first-order Einstein continuum equations in the Cartan formalism. It is shown that in the limit of small deficit angles these equations have Regge calculus, locally, as the only solution. A quantum measure is easily defined which does not suffer the ambiguities of Regge calculus, and a coupling with fermionic matter is easily introduced

Motivation and Study Habits of College Calculus Students: Does Studying Calculus in High School Make a Difference?

Science.gov (United States)

Gibson, Megan

2013-01-01

Due in part to the growing popularity of the Advanced Placement program, an increasingly large percentage of entering college students are enrolling in calculus courses having already taken calculus in high school. Many students do not score high enough on the AP calculus examination to place out of Calculus I, and many do not take the…

Hands-On Calculus

Science.gov (United States)

Sutherland, Melissa

2006-01-01

In this paper we discuss manipulatives and hands-on investigations for Calculus involving volume, arc length, and surface area to motivate and develop formulae which can then be verified using techniques of integration. Pre-service teachers in calculus courses using these activities experience a classroom in which active learning is encouraged and…

The malliavin calculus and related topics

CERN Document Server

Nualart, David

1995-01-01

The Malliavin calculus (or stochastic calculus of variations) is an infinite-dimensional differential calculus on the Wiener space Originally, it was developed to prove a probabilistic proof to Hörmander's "sum of squares" theorem, but more recently it has found application in a variety of stochastic differential equation problems This monograph presents the main features of the Malliavin calculus and discusses in detail its connection with the anticipating stochastic calculus The author begins by developing analysis on the Wiener space, and then uses this to analyze the regularity of probability laws and to prove Hörmander's theorem Subsequent chapters apply the Malliavin calculus to anticipating stochastic differential equations and to studying the Markov property of solutions to stochastic differential equations with boundary conditions

The Vectorial $\\lambda$-Calculus

OpenAIRE

Arrighi, Pablo; Díaz-Caro, Alejandro; Valiron, Benoît

2013-01-01

We describe a type system for the linear-algebraic $\\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\\lambda$-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We prove that the resulting typed $\\lambda$-calculus is strongly normalising and fea...

Collective enhancement of inclusive cross sections at large transverse momentum in stochastic-field multiparticle theory

International Nuclear Information System (INIS)

Arnold, R.C.

1976-01-01

A stochastic-field calculus, previously discussed in connection with Regge intercepts and instability questions, is applied to inclusive cross sections, and is shown to predict a growth with energy of large-P/perpendicular/ to inclusives

Teaching the Calculus

Science.gov (United States)

Sauerheber, Richard D.

2012-01-01

Methods of teaching the Calculus are presented in honour of Sir Isaac Newton, by discussing an extension of his original proofs and discoveries. The methods, requested by Newton to be used that reflect the historical sequence of the discovered Fundamental Theorems, allow first-time students to grasp quickly the basics of the Calculus from its…

Generalized vector calculus on convex domain

Science.gov (United States)

Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

Dental Calculus Arrest of Dental Caries.

Science.gov (United States)

Keyes, Paul H; Rams, Thomas E

An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. These observations further document the potential protective effects of dental calculus mineralization against dental caries.

Dental Calculus Arrest of Dental Caries

Science.gov (United States)

Keyes, Paul H.; Rams, Thomas E.

2016-01-01

Background An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. Materials and methods A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Results Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. Conclusions These observations further document the potential protective effects of dental calculus mineralization against dental caries. PMID:27446993

Pre-calculus workbook for dummies

CERN Document Server

Kuang, Yang

2011-01-01

Get the confidence and math skills you need to get started with calculus Are you preparing for calculus? This hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in the course. You'll get hundreds of valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every problem. You'll also memorize the most frequently used equations, see how to avoid common mistakes, understand tricky trig proofs, and much more. Pre-Calculus Workbook For Dummies is the perfect tool for anyone who wa

Initialized Fractional Calculus

Science.gov (United States)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.

Stochastic calculus in physics

International Nuclear Information System (INIS)

Fox, R.F.

1987-01-01

The relationship of Ito-Stratonovich stochastic calculus to studies of weakly colored noise is explained. A functional calculus approach is used to obtain an effective Fokker-Planck equation for the weakly colored noise regime. In a smooth limit, this representation produces the Stratonovich version of the Ito-Stratonovich calculus for white noise. It also provides an approach to steady state behavior for strongly colored noise. Numerical simulation algorithms are explored, and a novel suggestion is made for efficient and accurate simulation of white noise equations

Energy and Regge residues in quantum-mechanical ''QCD'' sum rules

International Nuclear Information System (INIS)

Durand, B.; Durand, L.

1986-01-01

It was shown recently by Fishbane, Kaus, and Gasiorowicz that the residues at the poles of quantum-mechanical two-point functions for arbitrary angular momenta l have an incorrect l dependence when calculated by the sum-rule method used for the analogous problem in QCD. Knowledge of the residues is of interest since they are directly related to particle couplings and decay widths. We develop reliable expressions for the energy and Regge residues using semiclassical methods

The stochastic quality calculus

DEFF Research Database (Denmark)

Zeng, Kebin; Nielson, Flemming; Nielson, Hanne Riis

2014-01-01

We introduce the Stochastic Quality Calculus in order to model and reason about distributed processes that rely on each other in order to achieve their overall behaviour. The calculus supports broadcast communication in a truly concurrent setting. Generally distributed delays are associated...... with the outputs and at the same time the inputs impose constraints on the waiting times. Consequently, the expected inputs may not be available when needed and therefore the calculus allows to express the absence of data.The communication delays are expressed by general distributions and the resulting semantics...

Advanced calculus

CERN Document Server

Nickerson, HK; Steenrod, NE

2011-01-01

""This book is a radical departure from all previous concepts of advanced calculus,"" declared the Bulletin of the American Mathematics Society, ""and the nature of this departure merits serious study of the book by everyone interested in undergraduate education in mathematics."" Classroom-tested in a Princeton University honors course, it offers students a unified introduction to advanced calculus. Starting with an abstract treatment of vector spaces and linear transforms, the authors introduce a single basic derivative in an invariant form. All other derivatives - gradient, divergent, curl,

Noncommutative operational calculus

Directory of Open Access Journals (Sweden)

Henry E. Heatherly

1999-12-01

Full Text Available Oliver Heaviside's operational calculus was placed on a rigorous mathematical basis by Jan Mikusinski, who constructed an algebraic setting for the operational methods. In this paper, we generalize Mikusi'{n}ski's methods to solve linear ordinary differential equations in which the unknown is a matrix- or linear operator-valued function. Because these functions can be zero-divisors and do not necessarily commute, Mikusi'{n}ski's one-dimensional calculus cannot be used. The noncommuative operational calculus developed here,however, is used to solve a wide class of such equations. In addition, we provide new proofs of existence and uniqueness theorems for certain matrix- and operator valued Volterra integral and integro-differential equations. Several examples are given which demonstrate these new methods.

Hexagon OPE resummation and multi-Regge kinematics

Energy Technology Data Exchange (ETDEWEB)

Drummond, J.M. [School of Physics & Astronomy, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom); Theory Division, Physics Department, CERN,CH-1211 Geneva 23 (Switzerland); LAPTh, CNRS, Université de Savoie,9 Chemin de Bellevue, F-74941 Annecy-le-Vieux Cedex (France); Papathanasiou, G. [LAPTh, CNRS, Université de Savoie,9 Chemin de Bellevue, F-74941 Annecy-le-Vieux Cedex (France)

2016-02-29

We analyse the OPE contribution of gluon bound states in the double scaling limit of the hexagonal Wilson loop in planar N=4 super Yang-Mills theory. We provide a systematic procedure for perturbatively resumming the contributions from single-particle bound states of gluons and expressing the result order by order in terms of two-variable polylogarithms. We also analyse certain contributions from two-particle gluon bound states and find that, after analytic continuation to the 2→4 Mandelstam region and passing to multi-Regge kinematics (MRK), only the single-particle gluon bound states contribute. From this double-scaled version of MRK we are able to reconstruct the full hexagon remainder function in MRK up to five loops by invoking single-valuedness of the results.

Differential Calculus on Quantum Spheres

OpenAIRE

Welk, Martin

1998-01-01

We study covariant differential calculus on the quantum spheres S_q^2N-1. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the quantum spheres, a framework of covariant differential calculus is established, including a particular first order calculus obtained by factorization, higher order calculi and a symmetry concept.

Baryon Regge trajectories from the area-law of Wilson loop

International Nuclear Information System (INIS)

Simonov, Yu.A.

1989-01-01

In the proper-time path integral representation of the three-quark Green function, baryon masses are calculated for large angular momenta L. Dynamics is given by vacuum background fields in the Wilson loop. Assuming an area law for large Wilson loops one obtains linear baryon Regge trajectories with the same slope as for mesons. For large L the baryon has an asymmetric structure of the quark-diquark type. Dynamic masses of the quark and diquark are generated, which grow with L. 8 refs

Disappearing renal calculus.

Science.gov (United States)

Cui, Helen; Thomas, Johanna; Kumar, Sunil

2013-04-10

We present a case of a renal calculus treated solely with antibiotics which has not been previously reported in the literature. A man with a 17 mm lower pole renal calculus and concurrent Escherichia coli urine infection was being worked up to undergo percutaneous nephrolithotomy. However, after a course of preoperative antibiotics the stone was no longer seen on retrograde pyelography or CT imaging.

Reasoning about objects using process calculus techniques

DEFF Research Database (Denmark)

Kleist, Josva

This thesis investigates the applicability of techniques known from the world of process calculi to reason about properties of object-oriented programs. The investigation is performed upon a small object-oriented language - The Sigma-calculus of Abadi and Cardelli. The investigation is twofold: We......-calculus turns out to be insufficient. Based on our experiences, we present a translation of a typed imperative Sigma-calculus, which looks promising. We are able to provide simple proofs of the equivalence of different Sigma-calculus objects using this translation. We use a labelled transition system adapted...... to the Sigma-calculus to investigate the use of process calculi techniques directly on the Sigma-calculus. The results obtained are of a fairly theoretical nature. We investigate the connection between the operational and denotaional semantics for a typed functional Sigma-calculus. The result is that Abadi...

Wilson loop, Regge trajectory and hadron masses in a Yang-Mills theory from semiclassical strings

International Nuclear Information System (INIS)

Bigazzi, F.; Cotrone, A.L.; Martucci, L.; Pando Zayas, L.A.

2004-07-01

We compute the one-loop string corrections to the Wilson loop, glueball Regge trajectory and stringy hadron masses in the Witten model of non supersymmetric, large-N Yang-Mills theory. The classical string configurations corresponding to the above field theory objects are respectively: open straight strings, folded closed spinning strings, and strings orbiting in the internal part of the supergravity background. For the rectangular Wilson loop we show that besides the standard Luscher term, string corrections provide a rescaling of the field theory string tension. The one-loop corrections to the linear glueball Regge trajectories render them nonlinear with a positive intercept, as in the experimental soft Pomeron trajectory. Strings orbiting in the internal space predict a spectrum of hadronic-like states charged under global flavor symmetries which falls in the same universality class of other confining models. (author)

Essential calculus with applications

CERN Document Server

Silverman, Richard A

1989-01-01

Rigorous but accessible text introduces undergraduate-level students to necessary background math, then clear coverage of differential calculus, differentiation as a tool, integral calculus, integration as a tool, and functions of several variables. Numerous problems and a supplementary section of ""Hints and Answers."" 1977 edition.

Pre-Calculus For Dummies

CERN Document Server

Kuang, Yang

2012-01-01

The fun and easy way to learn pre-calculus Getting ready for calculus but still feel a bit confused? Have no fear. Pre-Calculus For Dummies is an un-intimidating, hands-on guide that walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations. With this guide's help you'll quickly and painlessly get a handle on all of the concepts - not just the number crunching - and understand how to perform all pre-calc tasks, from graphing to tackling proofs. You'll also get a new appreciation for

Factors Associated with Success in College Calculus II

Science.gov (United States)

Rosasco, Margaret E.

2013-01-01

Students are entering college having earned credit for college Calculus 1 based on their scores on the College Board's Advanced Placement (AP) Calculus AB exam. Despite being granted credit for college Calculus 1, it is unclear whether these students are adequately prepared for college Calculus 2. College calculus classes are often taught from a…

String theory of the Regge intercept.

Science.gov (United States)

Hellerman, S; Swanson, I

2015-03-20

Using the Polchinski-Strominger effective string theory in the covariant gauge, we compute the mass of a rotating string in D dimensions with large angular momenta J, in one or two planes, in fixed ratio, up to and including first subleading order in the large J expansion. This constitutes a first-principles calculation of the value for the order-J(0) contribution to the mass squared of a meson on the leading Regge trajectory in planar QCD with bosonic quarks. For open strings with Neumann boundary conditions, and for closed strings in D≥5, the order-J(0) term in the mass squared is exactly calculated by the semiclassical approximation. This term in the expansion is universal and independent of the details of the theory, assuming only D-dimensional Poincaré invariance and the absence of other infinite-range excitations on the string world volume, beyond the Nambu-Goldstone bosons.

Leveraging Prior Calculus Study with Embedded Review

Science.gov (United States)

Nikolov, Margaret C.; Withers, Wm. Douglas

2016-01-01

We propose a new course structure to address the needs of college students with previous calculus study but no course validations as an alternative to repeating the first year of calculus. Students are introduced directly to topics from Calculus III unpreceded by a formal review of topics from Calculus I or II, but with additional syllabus time…

Open string Regge trajectory and its field theory limit

International Nuclear Information System (INIS)

Rojas, Francisco; Thorn, Charles B.

2011-01-01

We study the properties of the leading Regge trajectory in open string theory including the open string planar one-loop corrections. With SU(N) Chan-Paton factors, the sum over planar open string multiloop diagrams describes the 't Hooft limit N→∞ with Ng s 2 fixed. Our motivation is to improve the understanding of open string theory at finite α ' as a model of gauge field theories. SU(N) gauge theories in D space-time dimensions are described by requiring open strings to end on a stack of N Dp-branes of space-time dimension D=p+1. The large N leading trajectory α(t)=1+α ' t+Σ(t) can be extracted, through order g 2 , from the s→-∞ limit, at fixed t, of the four open string tree and planar loop diagrams. We analyze the t→0 behavior with the result that Σ(t)∼-Cg 2 (-α ' t) (D-4)/2 /(D-4). This result precisely tracks the 1-loop Reggeized gluon of gauge theory in D>4 space-time dimensions. In particular, for D→4 it reproduces the known infrared divergences of gauge theory in 4 dimensions with a Regge trajectory behaving as -ln(-α ' t). We also study Σ(t) in the limit t→-∞ and show that, when D ' t/(ln(-α ' t)) γ , where γ>0 depends on D and the number of massless scalars. Thus, as long as 4 ' t arbitrarily large. Finally we present the results of numerical calculations of Σ(t) for all negative t.

Unified treatment: analyticity, Regge trajectories, Veneziano amplitude, fundamental regions and Moebius transformations

International Nuclear Information System (INIS)

Choudhary, A.R.

2003-01-01

In this paper we present a unified treatment that combines the analyticity properties of the scattering amplitudes, the threshold and asymptotic behaviors, the invariance group of Moebius transformations, the automorphic functions defined over this invariance group, the fundamental region in (Poincare) geometry, and the generators of the invariance group as they relate to the fundamental region. Using these concepts and techniques, we provide a theoretical basis for Veneziano type amplitudes with the ghost elimination condition built in, related the Regge trajectory functions to the generators of the invariance group, constrained the values of the Regge trajectories to take only inverse integer values at the threshold, used the threshold behavior in the forward direction to deduce the Pomeranchuk trajectory as well as other relations. The enabling tool for this unified treatment came from the multi-sheet conformal mapping techniques that map the physical sheet to a fundamental region which in turn defines a Riemann surface on which a global uniformization variable for the scattering amplitude is calculated via an automorphic function, which in turn can be constructed as a quotient of two automorphic forms of the same dimension. (orig.)

Generalized Gaussian Error Calculus

CERN Document Server

Grabe, Michael

2010-01-01

For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large. The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions. The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence inter...

Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

Energy Technology Data Exchange (ETDEWEB)

Duca, Vittorio Del [Institute for Theoretical Physics, ETH Zürich,Hönggerberg, 8093 Zürich (Switzerland); Druc, Stefan; Drummond, James [School of Physics & Astronomy, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom); Duhr, Claude [Theoretical Physics Department, CERN,Route de Meyrin, CH-1211 Geneva 23 (Switzerland); Center for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, 1348 Louvain-La-Neuve (Belgium); Dulat, Falko [SLAC National Accelerator Laboratory, Stanford University,Stanford, CA 94309 (United States); Marzucca, Robin [Center for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, 1348 Louvain-La-Neuve (Belgium); Papathanasiou, Georgios [SLAC National Accelerator Laboratory, Stanford University,Stanford, CA 94309 (United States); Verbeek, Bram [Center for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, 1348 Louvain-La-Neuve (Belgium)

2016-08-25

We show that scattering amplitudes in planar N=4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes’ theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L+4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. Finally, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.

On the Presentation of Pre-Calculus and Calculus Topics: An Alternate View

Science.gov (United States)

Davydov, Aleksandr; Sturm-Beiss, Rachel

2008-01-01

The orders of presentation of pre-calculus and calculus topics, and the notation used, deserve careful study as they affect clarity and ultimately students' level of understanding. We introduce an alternate approach to some of the topics included in this sequence. The suggested alternative is based on years of teaching in colleges within and…

Quantum Variational Calculus

OpenAIRE

Malinowska , Agnieszka B.; Torres , Delfim

2014-01-01

International audience; Introduces readers to the treatment of the calculus of variations with q-differences and Hahn difference operators Provides the reader with the first extended treatment of quantum variational calculus Shows how the techniques described can be applied to economic models as well as other mathematical systems This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of it...

Laparoscopic Cholecystectomy in Chronic Calculus Cholecystitis

Directory of Open Access Journals (Sweden)

Prakash Sapkota

2013-12-01

Full Text Available Introduction: Laparoscopic cholecystectomy has clearly become the choice over open cholecystectomy in the treatment of hepatobiliary disease since its introduction by Mouret in 1987. This study evaluates a series of patients with chronic calculus cholecystitis who were treated with laparoscopic and open cholecystectomy and assesses the outcomes of both techniques. Objective: To evaluate the efficacy of laparoscopic vs open cholecystectomy in chronic calculus cholecystitis and establish the out-comes of this treatment modality at Lumbini Medical College and Teaching Hospital. Methods: This was a retrospective analysis over a one-year period (January 1, 2012 to December 31, 2012, per-formed by single surgeon at Lumbini Medical College and Teaching Hospital located midwest of Nepal. 166 patients underwent surgical treatment for chronic calculus cholecystitis. Patients included were only chronic calculus cholecystitis proven histopathologocally and the rest were excluded. Data was collected which included patients demographics, medical history, presentation, complications, conversion rates from laparoscopic. cholecystectomy to open cholecystectomy, operative and postoperative time. Results: Patients treated with laparoscopic cholecystectomy for chronic calculus cholecystitis had shorter operating times and length of stay compared to patients treated with open cholecystectomy for chronic calculus cholecystitis. Conversion rates were 3.54% in chronic calculus cholecystitis during the study period. Complications were also lower in patients who underwent laparoscopic cholecystectomy versus open cholecystectomy for cholelithiasis. Conclusions: Laparoscopic cholecystectomy appears to be a reliable, safe, and cost-effective treatment modality for chronic calculus cholecystitis.

Forward pion-nucleon charge exchange reaction and Regge constraints

International Nuclear Information System (INIS)

Huang Fei; Sibirtsev, A.; Krewald, S.; Hanhart, C.; Haidenbauer, J.; Meibner, U.-G.

2009-01-01

We present our recent study of pion-nucleon charge exchange amplitudes above 2 GeV. We analyze the forward pion-nucleon charge exchange reaction data in a Regge model and compare the resulting amplitudes with those from the Karlsruhe-Helsinki and George-Washington-University partial-wave analyses. We explore possible high-energy constraints for theoretical baryon resonance analyses in the energy region above 2 GeV. Our results show that for the pion-nucleon charge exchange reaction, the appropriate energy region for matching meson-nucleon dynamics to diffractive scattering should be around 3 GeV for the helicity flip amplitude. (authors)

A κ-symmetry calculus for superparticles

International Nuclear Information System (INIS)

Gauntlett, J.P.

1991-01-01

We develop a κ-symmetry calculus for the d=2 and d=3, N=2 massive superparticles, which enables us to construct higher order κ-invariant actions. The method relies on a reformulation of these models as supersymmetric sigma models that are invariant under local worldline superconformal transformations. We show that the κ-symmetry is embedded in the superconformal symmetry so that a calculus for the κ-symmetry is equivalent to a tensor calculus for the latter. We develop such a calculus without the introduction of a wordline supergravity multiplet. (orig.)

An AP Calculus Classroom Amusement Park

Science.gov (United States)

Ferguson, Sarah

2016-01-01

Throughout the school year, AP Calculus teachers strive to teach course content comprehensively and swiftly in an effort to finish all required material before the AP Calculus exam. As early May approaches and the AP Calculus test looms, students and teachers nervously complete lessons, assignments, and assessments to ensure student preparation.…

First Regge parameterisation of polarized DIS cross section

International Nuclear Information System (INIS)

Thomas, E.; Bianchi, N.

2000-01-01

The first Regge description of the virtual photon absorption cross section difference Δσ(γ*, N) = [σ 1/2 (γ*,N) - σ ((3)/(2)) (γ*, N)] was obtained from a global fit of all the data collected by the experiments measuring spin asymmetries in polarized lepton - polarized nucleon deep inelastic scattering. This work present a phenomenological and a numerical description of all the polarized deep inelastic data (Δσ(γ*, N), g l spin structure function) on the whole measured kinematical range (0.3 GeV 2 2 2 , 4 GeV 2 2 2 ). The fit also provide reliable predictions for the photo-production limit through a smooth Q 2 -transition

Discrete Ricci Flow in Higher Dimensions

Science.gov (United States)

2015-02-01

recently, we showed analytically that the SRF equations converged to the continuum RF equations for the neck-pinch 3- geometry [10]. In this analysis we also...Hamilton’s RF. It is the first dimensionally agnostic generalization of RF for PL geometries . We refer to our approach as simplicial Ricci flow (SRF). For a...Discrete Exterior Calculus , Regge Calculus , Piecewise Linear Complex 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT SAR 18. NUMBER

The time-oriented boundary states and the Lorentzian-spinfoam correlation functions

International Nuclear Information System (INIS)

Bianchi, Eugenio; Ding You

2012-01-01

A time-oriented semiclassical boundary state is introduced to calculate the correlation function in the Lorentzian Engle-Pereira-Rovelli-Livine spinfoam model. The resulting semiclassical correlation function is shown to match with the one in Regge calculus in a proper limit.

The untyped stack calculus and Bohm's theorem

Directory of Open Access Journals (Sweden)

Alberto Carraro

2013-03-01

Full Text Available The stack calculus is a functional language in which is in a Curry-Howard correspondence with classical logic. It enjoys confluence but, as well as Parigot's lambda-mu, does not admit the Bohm Theorem, typical of the lambda-calculus. We present a simple extension of stack calculus which is for the stack calculus what Saurin's Lambda-mu is for lambda-mu.

Discounted Duration Calculus

DEFF Research Database (Denmark)

Ody, Heinrich; Fränzle, Martin; Hansen, Michael Reichhardt

2016-01-01

To formally reason about the temporal quality of systems discounting was introduced to CTL and LTL. However, these logic are discrete and they cannot express duration properties. In this work we introduce discounting for a variant of Duration Calculus. We prove decidability of model checking...... for a useful fragment of discounted Duration Calculus formulas on timed automata under mild assumptions. Further, we provide an extensive example to show the usefulness of the fragment....

Introduction to the operational calculus

CERN Document Server

Berg, Lothar

2013-01-01

Introduction to the Operational Calculus is a translation of ""Einfuhrung in die Operatorenrechnung, Second Edition."" This book deals with Heaviside's interpretation, on the Laplace integral, and on Jan Mikusinki's fundamental work ""Operational Calculus."" Throughout the book, basic algebraic concepts appear as aids to understanding some relevant points of the subject. An important field for research in analysis is asymptotic properties. This text also discusses examples to show the potentialities in applying operational calculus that run beyond ordinary differential equations with constant

A Formal Calculus for Categories

DEFF Research Database (Denmark)

Cáccamo, Mario José

This dissertation studies the logic underlying category theory. In particular we present a formal calculus for reasoning about universal properties. The aim is to systematise judgements about functoriality and naturality central to categorical reasoning. The calculus is based on a language which...... extends the typed lambda calculus with new binders to represent universal constructions. The types of the languages are interpreted as locally small categories and the expressions represent functors. The logic supports a syntactic treatment of universality and duality. Contravariance requires a definition...... of universality generous enough to deal with functors of mixed variance. Ends generalise limits to cover these kinds of functors and moreover provide the basis for a very convenient algebraic manipulation of expressions. The equational theory of the lambda calculus is extended with new rules for the definitions...

Synthesizing controllers from duration calculus

DEFF Research Database (Denmark)

Fränzle, Martin

1996-01-01

Duration Calculus is a logic for reasoning about requirements for real-time systems at a high level of abstraction from operational detail, which qualifies it as an interesting starting point for embedded controller design. Such a design activity is generally thought to aim at a control device...... the physical behaviours of which satisfy the requirements formula, i.e. the refinement relation between requirements and implementations is taken to be trajectory inclusion. Due to the abstractness of the vocabulary of Duration Calculus, trajectory inclusion between control requirements and controller designs...... for embedded controller design and exploit this fact for developing an automatic procedure for controller synthesis from specifications formalized in Duration Calculus. As far as we know, this is the first positive result concerning feasibility of automatic synthesis from dense-time Duration Calculus....

Testicular calculus: A rare case.

Science.gov (United States)

Sen, Volkan; Bozkurt, Ozan; Demır, Omer; Tuna, Burcin; Yorukoglu, Kutsal; Esen, Adil

2015-01-01

Testicular calculus is an extremely rare case with unknown etiology and pathogenesis. To our knowledge, here we report the third case of testicular calculus. A 31-year-old man was admitted to our clinic with painful solid mass in left testis. After diagnostic work-up for a possible testicular tumour, he underwent inguinal orchiectomy and histopathologic examination showed a testicular calculus. Case hypothesis: Solid testicular lesions in young adults generally correspond to testicular cancer. Differential diagnosis should be done carefully. Future implications: In young adults with painful and solid testicular mass with hyperechogenic appearance on scrotal ultrasonography, testicular calculus must be kept in mind in differential diagnosis. Further reports on this topic may let us do more clear recommendations about the etiology and treatment of this rare disease.

The stack calculus

Directory of Open Access Journals (Sweden)

Alberto Carraro

2013-03-01

Full Text Available We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without any restriction. Its type system enforces strong normalization of expressions and it is a sound and complete system for full implicational Classical Logic. We give a very simple denotational semantics which allows easy calculations of the interpretation of expressions.

Improving student learning in calculus through applications

Science.gov (United States)

Young, C. Y.; Georgiopoulos, M.; Hagen, S. C.; Geiger, C. L.; Dagley-Falls, M. A.; Islas, A. L.; Ramsey, P. J.; Lancey, P. M.; Straney, R. A.; Forde, D. S.; Bradbury, E. E.

2011-07-01

Nationally only 40% of the incoming freshmen Science, Technology, Engineering and Mathematics (STEM) majors are successful in earning a STEM degree. The University of Central Florida (UCF) EXCEL programme is a National Science Foundation funded STEM Talent Expansion Programme whose goal is to increase the number of UCF STEM graduates. One of the key requirements for STEM majors is a strong foundation in Calculus. To improve student learning in calculus, the EXCEL programme developed two special courses at the freshman level called Applications of Calculus I (Apps I) and Applications of Calculus II (Apps II). Apps I and II are one-credit classes that are co-requisites for Calculus I and II. These classes are teams taught by science and engineering professors whose goal is to demonstrate to students where the calculus topics they are learning appear in upper level science and engineering classes as well as how faculty use calculus in their STEM research programmes. This article outlines the process used in producing the educational materials for the Apps I and II courses, and it also discusses the assessment results pertaining to this specific EXCEL activity. Pre- and post-tests conducted with experimental and control groups indicate significant improvement in student learning in Calculus II as a direct result of the application courses.

Quantum variational calculus

CERN Document Server

Malinowska, Agnieszka B

2014-01-01

This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete. Quantum Variational Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations fo...

Lacroix and the calculus

CERN Document Server

Domingues, João Caramalho

2008-01-01

Silvestre François Lacroix (Paris, 1765 - ibid., 1843) was a most influential mathematical book author. His most famous work is the three-volume Traité du calcul différentiel et du calcul intégral (1797-1800; 2nd ed. 1810-1819) – an encyclopedic appraisal of 18th-century calculus which remained the standard reference on the subject through much of the 19th century, in spite of Cauchy's reform of the subject in the 1820's. Lacroix and the Calculus is the first major study of Lacroix’s large Traité. It uses the unique and massive bibliography given by Lacroix to explore late 18th-century calculus, and the way it is reflected in Lacroix’s account. Several particular aspects are addressed in detail, including: the foundations of differential calculus, analytic and differential geometry, conceptions of the integral, and types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions). Lacroix’s large Traité... was a...

CLEP calculus

CERN Document Server

Hill, Gregory

2013-01-01

Earn College Credit with REA's Test Prep for CLEP* Calculus Everything you need to pass the exam and get the college credit you deserve.Our test prep for CLEP* Calculus and the free online tools that come with it, will allow you to create a personalized CLEP* study plan that can be customized to fit you: your schedule, your learning style, and your current level of knowledge.Here's how it works:Diagnostic exam at the REA Study Center focuses your studyOur online diagnostic exam pinpoints your strengths and shows you exactly where you need to focus your study. Armed with this information, you

A Higher-Order Calculus for Categories

DEFF Research Database (Denmark)

Cáccamo, Mario José; Winskel, Glynn

2001-01-01

A calculus for a fragment of category theory is presented. The types in the language denote categories and the expressions functors. The judgements of the calculus systematise categorical arguments such as: an expression is functorial in its free variables; two expressions are naturally isomorphic...... in their free variables. There are special binders for limits and more general ends. The rules for limits and ends support an algebraic manipulation of universal constructions as opposed to a more traditional diagrammatic approach. Duality within the calculus and applications in proving continuity are discussed...... with examples. The calculus gives a basis for mechanising a theory of categories in a generic theorem prover like Isabelle....

The calculus primer

CERN Document Server

Schaaf, William L

2011-01-01

Comprehensive but concise, this introduction to differential and integral calculus covers all the topics usually included in a first course. The straightforward development places less emphasis on mathematical rigor, and the informal manner of presentation sets students at ease. Many carefully worked-out examples illuminate the text, in addition to numerous diagrams, problems, and answers.Bearing the needs of beginners constantly in mind, the treatment covers all the basic concepts of calculus: functions, derivatives, differentiation of algebraic and transcendental functions, partial different

Computing for calculus

CERN Document Server

Christensen, Mark J

1981-01-01

Computing for Calculus focuses on BASIC as the computer language used for solving calculus problems.This book discusses the input statement for numeric variables, advanced intrinsic functions, numerical estimation of limits, and linear approximations and tangents. The elementary estimation of areas, numerical and string arrays, line drawing algorithms, and bisection and secant method are also elaborated. This text likewise covers the implicit functions and differentiation, upper and lower rectangular estimates, Simpson's rule and parabolic approximation, and interpolating polynomials. Other to

Putting Differentials Back into Calculus

Science.gov (United States)

Dray, Tevian; Manogue, Corrine A.

2010-01-01

We argue that the use of differentials in introductory calculus courses is useful and provides a unifying theme, leading to a coherent view of the calculus. Along the way, we meet several interpretations of differentials, some better than others.

Giant calculus: review and report of a case.

Science.gov (United States)

Woodmansey, Karl; Severine, Anthony; Lembariti, Bakari S

2013-01-01

Dental calculus is a common oral finding. The term giant calculus is used to describe unusually large deposits of dental calculus. Several extreme cases have been reported in the dental literature. The specific etiology of these cases remains uncertain. This paper reviews previously reported cases, and presents another extreme example of giant calculus.

The two-loop symbol of all multi-Regge regions

International Nuclear Information System (INIS)

Bargheer, Till; Papathanasiou, Georgios; Schomerus, Volker

2016-01-01

We study the symbol of the two-loop n-gluon MHV amplitude for all Mandelstam regions in multi-Regge kinematics in N=4 super Yang-Mills theory. While the number of distinct Mandelstam regions grows exponentially with n, the increase of independent symbols turns out to be merely quadratic. We uncover how to construct the symbols for any number of external gluons from just two building blocks which are naturally associated with the six- and seven-gluon amplitude, respectively. The second building block is entirely new, and in addition to its symbol, we also construct a prototype function that correctly reproduces all terms of maximal functional transcendentality.

The two-loop symbol of all multi-Regge regions

International Nuclear Information System (INIS)

Bargheer, Till; Schomerus, Volker; Papathanasiou, Georgios

2015-12-01

We study the symbol of the two-loop n-gluon MHV amplitude for all Mandelstam regions in multi-Regge kinematics in N= 4 super Yang-Mills theory. While the number of distinct Mandelstam regions grows exponentially with n, the increase of independent symbols turns out to be merely quadratic. We uncover how to construct the symbols for any number of external gluons from just two building blocks which are naturally associated with the six- and seven-gluon amplitude, respectively. The second building block is entirely new, and in addition to its symbol, we also construct a prototype function that correctly reproduces all terms of maximal functional transcendentality.

Calculus with vectors

CERN Document Server

Treiman, Jay S

2014-01-01

Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM. fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises. All three-dimensional graphs have rotatable versions included as extra source materials and may be freely downloaded and manipulated with Maple Player; a free Maple Player App is available for the iPad on iTunes. The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits, and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additio...

Regge behavior saves string theory from causality violations

DEFF Research Database (Denmark)

di Vecchia, Paolo; Giuseppe, D'Appollonio; Russo, Rodolfo

2015-01-01

Higher-derivative corrections to the Einstein-Hilbert action are present in bosonic string theory leading to the potential causality violations recently pointed out by Camanho et al. [1]. We analyze in detail this question by considering high-energy string-brane collisions at impact parameters b....... Such violations are instead neatly avoided when the full structure of string theory — and in particular its Regge behavior — is taken into account....... ≤ l s (the string-length parameter) with l s ≫ R p (the characteristic scale of the Dp-brane geometry). If we keep only the contribution of the massless states causality is violated for a set of initial states whose polarization is suitably chosen with respect to the impact parameter vector...

Calculus and analysis in Euclidean space

CERN Document Server

Shurman, Jerry

2016-01-01

The graceful role of analysis in underpinning calculus is often lost to their separation in the curriculum. This book entwines the two subjects, providing a conceptual approach to multivariable calculus closely supported by the structure and reasoning of analysis. The setting is Euclidean space, with the material on differentiation culminating in the inverse and implicit function theorems, and the material on integration culminating in the general fundamental theorem of integral calculus. More in-depth than most calculus books but less technical than a typical analysis introduction, Calculus and Analysis in Euclidean Space offers a rich blend of content to students outside the traditional mathematics major, while also providing transitional preparation for those who will continue on in the subject. The writing in this book aims to convey the intent of ideas early in discussion. The narrative proceeds through figures, formulas, and text, guiding the reader to do mathematics resourcefully by marshaling the skil...

Dental calculus detection using the VistaCam.

Science.gov (United States)

Shakibaie, Fardad; Walsh, Laurence J

2016-12-01

The VistaCam® intra-oral camera system (Dürr Dental, Bietigheim-Bissingen, Germany) is a fluorescence system using light emitting diodes that produce a 405-nm violet light. This wavelength has potential application for detection of dental calculus based on red emissions from porphyrin molecules. This study assessed the digital scores obtained for both supragingival and subgingival calculus on 60 extracted teeth and compared these with lesions of dental caries. It has also examined the effect of saliva and blood on the fluorescence readings for dental calculus. VistaCam fluorescence scores for both supragingival (1.7-3.3) and subgingival calculus (1.3-2.4) were higher than those for sound root surfaces (0.9-1.1) and dental caries (0.9-2.2) ( p  calculus samples were not affected by the presence of saliva or blood. These results suggest that the use of violet light fluorescence could be a possible adjunct to clinical examination for deposits of dental calculus.

A new approach to perturbative and non-perturbative dynamics: Regge intercept and the gluon spin

International Nuclear Information System (INIS)

Bishari, M.

1979-01-01

Relations connecting long distance with short distance dynamics are proposed. These relations are independent of the (apiori unknown) matching length scale, and provide interrelations among parameters characterizing soft and hard scattering processes. In particular, the observed planar Regge intercept imply an underlying field theory mediated by vector gluons. (author)

Two-dimensional calculus

CERN Document Server

Osserman, Robert

2011-01-01

The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o

On Some Syntactic Properties of the Modalized Heyting Calculus

OpenAIRE

Muravitsky, Alexei

2016-01-01

We show that the modalized Heyting calculus introduced by Leo Esakia admits a normal axiomatization. Then, we prove that the inference rules $\\square\\alpha/\\alpha$ and $\\square\\alpha\\rightarrow\\alpha/\\alpha$ are admissible in this calculus. Finally, we show that this calculus and intuitionistic propositional calculus are assertorically equipollent, which leads to a variant of limited separation property for the modalized Heyting calculus.

The calculus a genetic approach

CERN Document Server

Toeplitz, Otto

2007-01-01

When first published posthumously in 1963, this book presented a radically different approach to the teaching of calculus.  In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique a

Pre-calculus workbook for dummies

CERN Document Server

Gilman, Michelle Rose; Neal, Karina

2009-01-01

Get the confidence and the math skills you need to get started with calculus! Are you preparing for calculus? This easy-to-follow, hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in your cour sework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every problem. You'll also memorize the most frequently used equations, see how to avoid common mistakes, understand tricky trig proofs, and much more. 100s of Problems! Detailed, fully worked-out solutions to problem

Mathematics for physics with calculus

CERN Document Server

Das, Biman

2005-01-01

Designed for students who plan to take or who are presently taking calculus-based physics courses. This book will develop necessary mathematical skills and help students gain the competence to use precalculus, calculus, vector algebra, vector calculus, and the statistical analysis of experimental data. Students taking intermediate physics, engineering, and other science courses will also find the book useful-and will be able to use the book as a mathematical resource for these intermediate level courses. The book emphasizes primarily the use of mathematical techniques and mathematical concepts in Physics and does not go into their rigorous developments.

On exterior variational calculus

International Nuclear Information System (INIS)

Aldrovandi, R.; Kraenkel, R.A.

1987-01-01

Exterior variational calculus is introduced through examples in field theory. It provides a very simple technique to decide on the existence of Lagrangians for given equations of motions and, in the case, to find them. Only local aspects are discussed but the analogy to exterior calculus on finite dimensional manifolds is complete, strongly suggesting its suitability to the study of topological aspects. (Author) [pt

ASSESSING STUDENTS' UNDERSTANDING OF PRE-CALCULUS CONCEPTS

OpenAIRE

Dr. Jyoti Sharma

2017-01-01

Calculus is one of the most momentous achievements of the human intellect (Boyer, 1949). It has given a new direction to the work of mathematicians and scientists. Calculus has exponentially expanded the scope and use of mathematics in other fields. Learning calculus is important to pursue career in applied mathematics.

Dental Calculus Arrest of Dental Caries

OpenAIRE

Keyes, Paul H.; Rams, Thomas E.

2016-01-01

Background An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human t...

Jet-calculus approach including coherence effects

International Nuclear Information System (INIS)

Jones, L.M.; Migneron, R.; Narayanan, K.S.S.

1987-01-01

We show how integrodifferential equations typical of jet calculus can be combined with an averaging procedure to obtain jet-calculus-based results including the Mueller interference graphs. Results in longitudinal-momentum fraction x for physical quantities are higher at intermediate x and lower at large x than with the conventional ''incoherent'' jet calculus. These results resemble those of Marchesini and Webber, who used a Monte Carlo approach based on the same dynamics

Functional Fractional Calculus

CERN Document Server

Das, Shantanu

2011-01-01

When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with 'ordinary' differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematic

A primer on exterior differential calculus

Directory of Open Access Journals (Sweden)

Burton D.A.

2003-01-01

Full Text Available A pedagogical application-oriented introduction to the cal­culus of exterior differential forms on differential manifolds is presented. Stokes' theorem, the Lie derivative, linear con­nections and their curvature, torsion and non-metricity are discussed. Numerous examples using differential calculus are given and some detailed comparisons are made with their tradi­tional vector counterparts. In particular, vector calculus on R3 is cast in terms of exterior calculus and the traditional Stokes' and divergence theorems replaced by the more powerful exterior expression of Stokes' theorem. Examples from classical continuum mechanics and spacetime physics are discussed and worked through using the language of exterior forms. The numerous advantages of this calculus, over more traditional ma­chinery, are stressed throughout the article. .

Model-checking dense-time Duration Calculus

DEFF Research Database (Denmark)

Fränzle, Martin

2004-01-01

Since the seminal work of Zhou Chaochen, M. R. Hansen, and P. Sestoft on decidability of dense-time Duration Calculus [Zhou, Hansen, Sestoft, 1993] it is well-known that decidable fragments of Duration Calculus can only be obtained through withdrawal of much of the interesting vocabulary...... of this logic. While this was formerly taken as an indication that key-press verification of implementations with respect to elaborate Duration Calculus specifications were also impossible, we show that the model property is well decidable for realistic designs which feature natural constraints...... suitably sparser model classes we obtain model-checking procedures for rich subsets of Duration Calculus. Together with undecidability results also obtained, this sheds light upon the exact borderline between decidability and undecidability of Duration Calculi and related logics....

Analysis of the logarithmic slope of F2 from the Regge gluon density behavior at small x

International Nuclear Information System (INIS)

Boroun, G. R.

2010-01-01

We study the accuracy of the Regge behavior of the gluon distribution function for an approximate relation that is frequently used to extract the logarithmic slopes of the structure function from the gluon distribution at small x. We show that the Regge behavior analysis results are comparable with HERA data and are also better than other methods that expand the gluon density at distinct points of expansion. We also show that for Q 2 = 22.4 GeV 2 , the x dependence of the data is well described by gluon shadowing corrections to the GLR-MQ equation. The resulting analytic expression allows us to predict the logarithmic derivative ∂F 2 (x, Q 2 )/∂lnQ 2 and to compare the results with the H1 data and a QCD analysis fit with the MRST parameterization input.

Proof Nets for Lambek Calculus

NARCIS (Netherlands)

Roorda, Dirk

1992-01-01

The proof nets of linear logic are adapted to the non-commutative Lambek calculus. A different criterion for soundness of proof nets is given, which gives rise to new algorithms for proof search. The order sensitiveness of the Lambek calculus is reflected by the planarity condition on proof nets;

On the fractional calculus of Besicovitch function

International Nuclear Information System (INIS)

Liang Yongshun

2009-01-01

Relationship between fractional calculus and fractal functions has been explored. Based on prior investigations dealing with certain fractal functions, fractal dimensions including Hausdorff dimension, Box dimension, K-dimension and Packing dimension is shown to be a linear function of order of fractional calculus. Both Riemann-Liouville fractional calculus and Weyl-Marchaud fractional derivative of Besicovitch function have been discussed.

The Calculus of a Vase

Science.gov (United States)

Scherger, Nicole

2012-01-01

Of the most universal applications in integral calculus are those involved with finding volumes of solids of revolution. These profound problems are typically taught with traditional approaches of the disk and shell methods, after which most calculus curriculums will additionally cover arc length and surfaces of revolution. Even in these visibly…

Miniature endoscopic optical coherence tomography for calculus detection.

Science.gov (United States)

Kao, Meng-Chun; Lin, Chun-Li; Kung, Che-Yen; Huang, Yi-Fung; Kuo, Wen-Chuan

2015-08-20

The effective treatment of periodontitis involves the detection and removal of subgingival dental calculus. However, subgingival calculus is more difficult to detect than supragingival calculus because it is firmly attached to root surfaces within periodontal pockets. To achieve a smooth root surface, clinicians often remove excessive amounts of root structure because of decreased visibility. In addition, enamel pearl, a rare type of ectopic enamel formation on the root surface, can easily be confused with dental calculus in the subgingival environment. In this study, we developed a fiber-probe swept-source optical coherence tomography (SSOCT) technique and combined it with the quantitative measurement of an optical parameter [standard deviation (SD) of the optical coherence tomography (OCT) intensity] to differentiate subgingival calculus from sound enamel, including enamel pearl. Two-dimensional circumferential images were constructed by rotating the miniprobe (0.9 mm diameter) while acquiring image lines, and the adjacent lines in each rotation were stacked to generate a three-dimensional volume. In OCT images, compared to sound enamel and enamel pearls, dental calculus showed significant differences (Pdental calculus.

Applications of fractional calculus in physics

CERN Document Server

2000-01-01

Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and co

Enriching an effect calculus with linear types

DEFF Research Database (Denmark)

Egger, Jeff; Møgelberg, Rasmus Ejlers; Simpson, Alex

2009-01-01

We define an ``enriched effect calculus'' by conservatively extending  a type theory for computational effects with primitives from linear logic. By doing so, we obtain a generalisation of linear type theory, intended as a formalism for expressing linear aspects of effects. As a worked example, we...... formulate  linearly-used continuations in the enriched effect calculus. These are captured by a fundamental translation of the enriched effect calculus into itself, which extends existing call-by-value and call-by-name linearly-used CPS translations. We show that our translation is involutive. Full...... completeness results for the various linearly-used CPS translations  follow. Our main results, the conservativity of enriching the effect calculus with linear primitives, and the involution property of the fundamental translation, are proved using a category-theoretic semantics for the enriched effect calculus...

Detection, removal and prevention of calculus: Literature Review

Directory of Open Access Journals (Sweden)

Deepa G. Kamath

2014-01-01

Full Text Available Dental plaque is considered to be a major etiological factor in the development of periodontal disease. Accordingly, the elimination of supra- and sub-gingival plaque and calculus is the cornerstone of periodontal therapy. Dental calculus is mineralized plaque; because it is porous, it can absorb various toxic products that can damage the periodontal tissues. Hence, calculus should be accurately detected and thoroughly removed for adequate periodontal therapy. Many techniques have been used to identify and remove calculus deposits present on the root surface. The purpose of this review was to compile the various methods and their advantages for the detection and removal of calculus.

General quantum variational calculus

Directory of Open Access Journals (Sweden)

Artur M. C. Brito da Cruz

2018-02-01

Full Text Available We develop a new variational calculus based in the general quantum difference operator recently introduced by Hamza et al. In particular, we obtain optimality conditions for generalized variational problems where the Lagrangian may depend on the endpoints conditions and a real parameter, for the basic and isoperimetric problems, with and without fixed boundary conditions. Our results provide a generalization to previous results obtained for the $q$- and Hahn-calculus.

Łukasiewicz mu-Calculus

Directory of Open Access Journals (Sweden)

Matteo Mio

2013-08-01

Full Text Available The paper explores properties of Łukasiewicz mu-calculus, a version of the quantitative/probabilistic modal mu-calculus containing both weak and strong conjunctions and disjunctions from Łukasiewicz (fuzzy logic. We show that this logic encodes the well-known probabilistic temporal logic PCTL. And we give a model-checking algorithm for computing the rational denotational value of a formula at any state in a finite rational probabilistic nondeterministic transition system.

Calculus of bivariant function

OpenAIRE

PTÁČNÍK, Jan

2011-01-01

This thesis deals with the introduction of function of two variables and differential calculus of this function. This work should serve as a textbook for students of elementary school's teacher. Each chapter contains a summary of basic concepts and explanations of relationships, then solved model exercises of the topic and finally the exercises, which should solve the student himself. Thesis have transmit to students basic knowledges of differential calculus of functions of two variables, inc...

Geometric calculus: a new computational tool for Riemannian geometry

International Nuclear Information System (INIS)

Moussiaux, A.; Tombal, P.

1988-01-01

We compare geometric calculus applied to Riemannian geometry with Cartan's exterior calculus method. The correspondence between the two methods is clearly established. The results obtained by a package written in an algebraic language and doing general manipulations on multivectors are compared. We see that the geometric calculus is as powerful as exterior calculus

Boundary actions in Ponzano-Regge discretization, Quantum groups and AdS(3)

OpenAIRE

O'Loughlin, Martin

2000-01-01

Boundary actions for three-dimensional quantum gravity in the discretized formalism of Ponzano-Regge are studied with a view towards understanding the boundary degrees of freedom. These degrees of freedom postulated in the holography hypothesis are supposed to be characteristic of quantum gravity theories. In particular it is expected that some of these degrees of freedom reside on black hole horizons. This paper is a study of these ideas in the context of a theory of quantum gravity that req...

Proton-proton total cross sections and the neglect of masses in data fitting in the Regge region

International Nuclear Information System (INIS)

Kamran, M.

1981-01-01

It is shown by taking the example of pp total cross sections that the use of the approximation s is appoximately equal to 2qsup(1/2) while fitting data in the Regge region can be misleading. Several standard fits to sigmasub(tot)pp data are based on the assumption of weak rho-f-ω-A 2 exchange degeneracy (EXD). However, these fits involve the use of the approximation mentioned. It is found that it is impossible to fit the sigmasub(tot)pp data in the range 6 2 EXD. This investigation shows that sigmasub(tot)pp data alone seem to indicate either a breaking of weak rho-f-ω-A 2 EXD or the presence of low-lying contributions, or both, provided the masses of the interacting particles in data fitting in the Regge region ((Pi)ab>=5GeV/c) are not ignored

Fluorescence detection of dental calculus

International Nuclear Information System (INIS)

Gonchukov, S; Sukhinina, A; Vdovin, Yu; Biryukova, T

2010-01-01

This work is devoted to the optimization of fluorescence dental calculus diagnostics in optical spectrum. The optimal wavelengths for fluorescence excitation and registration are determined. Two spectral ranges 620 – 645 nm and 340 – 370 nm are the most convenient for supra- and subgingival calculus determination. The simple implementation of differential method free from the necessity of spectrometer using was investigated. Calculus detection reliability in the case of simple implementation is higher than in the case of spectra analysis at optimal wavelengths. The use of modulated excitation light and narrowband detection of informative signal allows us to decrease essentially its diagnostic intensity even in comparison with intensity of the low level laser dental therapy

Fluorescence detection of dental calculus

Science.gov (United States)

Gonchukov, S.; Biryukova, T.; Sukhinina, A.; Vdovin, Yu

2010-11-01

This work is devoted to the optimization of fluorescence dental calculus diagnostics in optical spectrum. The optimal wavelengths for fluorescence excitation and registration are determined. Two spectral ranges 620 - 645 nm and 340 - 370 nm are the most convenient for supra- and subgingival calculus determination. The simple implementation of differential method free from the necessity of spectrometer using was investigated. Calculus detection reliability in the case of simple implementation is higher than in the case of spectra analysis at optimal wavelengths. The use of modulated excitation light and narrowband detection of informative signal allows us to decrease essentially its diagnostic intensity even in comparison with intensity of the low level laser dental therapy.

Essential AOP: The A Calculus

DEFF Research Database (Denmark)

De Fraine, Bruno; Ernst, Erik; Südholt, Mario

2012-01-01

Aspect-oriented programming (AOP) has produced interesting language designs, but also ad hoc semantics that needs clarification. We contribute to this clarification with a calculus that models essential AOP, both simpler and more general than existing formalizations. In AOP, advice may intercept......-oriented code. Two well-known pointcut categories, call and execution, are commonly considered similar.We formally expose their differences, and resolve the associated soundness problem. Our calculus includes type ranges, an intuitive and concise alternative to explicit type variables that allows advice...... to be polymorphic over intercepted methods. We use calculus parameters to cover type safety for a wide design space of other features. Type soundness is verified in Coq....

Topology, calculus and approximation

CERN Document Server

Komornik, Vilmos

2017-01-01

Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...

Can the "standard" unitarized Regge models describe the TOTEM data?

CERN Document Server

Alkin, A; Martynov, E

2013-01-01

The standard Regge poles are considered as inputs for two unitarization methods: eikonal and U-matrix. It is shown that only models with three input pomerons and two input odderons can describe the high energy data on $pp$ and $\\bar pp$ elastic scattering including the new data from Tevatron and LHC. However, it seems that the both considered models require a further modification (e.g. nonlinear reggeon trajectories and/or nonexponential vertex functions) for a more satisfactory description of the data at 19.0 GeV$\\leq \\sqrt{s}\\leq$ 7 TeV and 0.01 $\\leq |t|\\leq $14.2 GeV$^{2}$.

Recursive sequences in first-year calculus

Science.gov (United States)

Krainer, Thomas

2016-02-01

This article provides ready-to-use supplementary material on recursive sequences for a second-semester calculus class. It equips first-year calculus students with a basic methodical procedure based on which they can conduct a rigorous convergence or divergence analysis of many simple recursive sequences on their own without the need to invoke inductive arguments as is typically required in calculus textbooks. The sequences that are accessible to this kind of analysis are predominantly (eventually) monotonic, but also certain recursive sequences that alternate around their limit point as they converge can be considered.

Success in Introductory Calculus: The Role of High School and Pre-calculus Preparation

OpenAIRE

Ayebo, Abraham; Ukkelberg, Sarah; Assuah, Charles

2017-01-01

Calculus at the college level has significantpotential to serve as a pump for increasing the number of students majoring inSTEM fields. It is a foundation course for all STEM majors and, if mastered well,should provide students with a positive and successful first-year experienceand gateway into more advanced courses. Studies have shown that a high percentage of studentsfailing college calculus has caused a shortage of individuals entering fieldsthat are heavily dependent on mathematics. Many...

Dental calculus image based on optical coherence tomography

Science.gov (United States)

Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei

2011-03-01

In this study, the dental calculus was characterized and imaged by means of swept-source optical coherence tomography (SSOCT). The refractive indices of enamel, dentin, cementum and calculus were measured as 1.625+/-0.024, 1.534+/-0.029, 1.570+/-0.021 and 1.896+/-0.085, respectively. The dental calculus lead strong scattering property and thus the region can be identified under enamel with SSOCT imaging. An extracted human tooth with calculus was covered by gingiva tissue as in vitro sample for SSOCT imaging.

Calculus detection technologies: where do we stand now?

Science.gov (United States)

Archana, V

2014-01-01

Epidemiological studies have implicated dental calculus as an ideal substrate for subgingival microbial colonization. Therefore, the main objective of periodontal therapy is to eliminate the microbial biofilm along with the calculus deposits from the root surface by root surface debridement. Over the past years, a large number of clinical and laboratory studies have been conducted to evaluate the efficacy of calculus removal by various methods. None of these conventional methods or devices was effective in completely eliminating all the calculus from the diseased root surfaces. In this context, a number of newer technologies have been developed to identify and selectively remove the dental calculus. Regarding this fact, the present article highlights a critical review of these devices based on published clinical and experimental data.

Calculus detection technologies: where do we stand now?

Science.gov (United States)

Archana, V

2014-01-01

Epidemiological studies have implicated dental calculus as an ideal substrate for subgingival microbial colonization. Therefore, the main objective of periodontal therapy is to eliminate the microbial biofilm along with the calculus deposits from the root surface by root surface debridement. Over the past years, a large number of clinical and laboratory studies have been conducted to evaluate the efficacy of calculus removal by various methods. None of these conventional methods or devices was effective in completely eliminating all the calculus from the diseased root surfaces. In this context, a number of newer technologies have been developed to identify and selectively remove the dental calculus. Regarding this fact, the present article highlights a critical review of these devices based on published clinical and experimental data. PMID:25870667

Characteristics of subgingival calculus detection by multiphoton fluorescence microscopy

Science.gov (United States)

Tung, Oi-Hong; Lee, Shyh-Yuan; Lai, Yu-Lin; Chen, How-Foo

2011-06-01

Subgingival calculus has been recognized as a major cause of periodontitis, which is one of the main chronic infectious diseases of oral cavities and a principal cause of tooth loss in humans. Bacteria deposited in subgingival calculus or plaque cause gingival inflammation, function deterioration, and then periodontitis. However, subgingival calculus within the periodontal pocket is a complicated and potentially delicate structure to be detected with current dental armamentaria, namely dental x-rays and dental probes. Consequently, complete removal of subgingival calculus remains a challenge to periodontal therapies. In this study, the detection of subgingival calculus employing a multiphoton autofluorescence imaging method was characterized in comparison with a one-photon confocal fluorescence imaging technique. Feasibility of such a system was studied based on fluorescence response of gingiva, healthy teeth, and calculus with and without gingiva covered. The multiphoton fluorescence technology perceived the tissue-covered subgingival calculus that cannot be observed by the one-photon confocal fluorescence method.

Dental calculus formation in children and adolescents undergoing hemodialysis.

Science.gov (United States)

Martins, Carla; Siqueira, Walter Luiz; Oliveira, Elizabeth; Nicolau, José; Primo, Laura Guimarães

2012-10-01

This study aimed to determine whether dental calculus formation is really higher among patients with chronic kidney disease undergoing hemodialysis than among controls. Furthermore, the study evaluated correlations between dental calculus formation and dental plaque, variables that are related to renal disease and/or saliva composition. The Renal Group was composed of 30 patients undergoing hemodialysis, whereas the Healthy Group had 30 clinically healthy patients. Stimulated whole saliva and parotid saliva were collected. Salivary flow rate and calcium and phosphate concentrations were determined. In the Renal Group the saliva collection was carried out before and after a hemodialysis session. Patients from both groups received intraoral exams, oral hygiene instructions, and dental scaling. Three months later, the dental calculus was measured by the Volpe-Manhold method to determine the rate of dental calculus formation. The Renal Group presented a higher rate of dental calculus formation (p dental calculus formation and whole saliva flow rate in the Renal Group after a hemodialysis session (r = 0.44, p dental calculus was associated with phosphate concentration in whole saliva from the Renal Group (p dental calculus formation, probably due to salivary variables.

Fluorescence spectroscopy of dental calculus

International Nuclear Information System (INIS)

Bakhmutov, D; Gonchukov, S; Sukhinina, A

2010-01-01

The aim of the present study was to investigate the fluorescence properties of dental calculus in comparison with the properties of adjacent unaffected tooth structure using both lasers and LEDs in the UV-visible range for fluorescence excitation. The influence of calculus color on the informative signal is demonstrated. The optimal spectral bands of excitation and registration of the fluorescence are determined

Fluorescence spectroscopy of dental calculus

Science.gov (United States)

Bakhmutov, D.; Gonchukov, S.; Sukhinina, A.

2010-05-01

The aim of the present study was to investigate the fluorescence properties of dental calculus in comparison with the properties of adjacent unaffected tooth structure using both lasers and LEDs in the UV-visible range for fluorescence excitation. The influence of calculus color on the informative signal is demonstrated. The optimal spectral bands of excitation and registration of the fluorescence are determined.

Brownian motion, martingales, and stochastic calculus

CERN Document Server

Le Gall, Jean-François

2016-01-01

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...

A Calculus of Communicating Systems with Label Passing

DEFF Research Database (Denmark)

Engberg, Uffe Henrik; Nielsen, Mogens

Milner's Calculus of Communicating Systems (CCS) is extended with a mechanism for label passing - as an attempt to remedy some of the shortcomings of CCS w.r.t. dynamic change of agent interconnections. In the extended calculus, restriction is viewed formally as a binder, and the calculus allows...... dynamic change of scope (of label) in connection with communication. It is proved that algebraic properties of strong (and observational) equivalence for CCS are preserved by the extension. Examples illustrating the expressive power of the calculus and its methods for reasoning are given....

Multiplicative calculus in biomedical image analysis

NARCIS (Netherlands)

Florack, L.M.J.; Assen, van H.C.

2011-01-01

We advocate the use of an alternative calculus in biomedical image analysis, known as multiplicative (a.k.a. non-Newtonian) calculus. It provides a natural framework in problems in which positive images or positive definite matrix fields and positivity preserving operators are of interest. Indeed,

A type system for continuation calculus

NARCIS (Netherlands)

Geuvers, J.H.; Geraedts, W.; Geron, B.; Stegeren, van J.; Oliva, P.

2014-01-01

Continuation Calculus (CC), introduced by Geron and Geuvers, is a simple foundational model for functional computation. It is closely related to lambda calculus and term rewriting, but it has no variable binding and no pattern matching. It is Turing complete and evaluation is deterministic. Notions

Regularities in hadron systematics, Regge trajectories and a string quark model

International Nuclear Information System (INIS)

Chekanov, S.V.; Levchenko, B.B.

2006-08-01

An empirical principle for the construction of a linear relationship between the total angular momentum and squared-mass of baryons is proposed. In order to examine linearity of the trajectories, a rigorous least-squares regression analysis was performed. Unlike the standard Regge-Chew-Frautschi approach, the constructed trajectories do not have non-linear behaviour. A similar regularity may exist for lowest-mass mesons. The linear baryonic trajectories are well described by a semi-classical picture based on a spinning relativistic string with tension. The obtained numerical solution of this model was used to extract the (di)quark masses. (orig.)

Differential calculus on deformed E(2) group

International Nuclear Information System (INIS)

Giller, S.; Gonera, C.; Kosinski, P.; Maslanka, P.

1997-01-01

Four dimensional bi-covariant differential *-calculus on quantum E(2) group is constructed. The relevant Lie algebra is obtained and covariant differential calculus on quantum plane is found. (author)

Restricted diversity of dental calculus methanogens over five centuries, France

OpenAIRE

Hong T. T. Huynh; Vanessa D. Nkamga; Michel Signoli; Stéfan Tzortzis; Romuald Pinguet; Gilles Audoly; Gérard Aboudharam; Michel Drancourt

2016-01-01

Methanogens are acknowledged archaeal members of modern dental calculus microbiota and dental pathogen complexes. Their repertoire in ancient dental calculus is poorly known. We therefore investigated archaea in one hundred dental calculus specimens collected from individuals recovered from six archaeological sites in France dated from the 14th to 19th centuries AD. Dental calculus was demonstrated by macroscopic and cone-beam observations. In 56 calculus specimens free of PCR inhibition, PCR...

Regge pole plus cut model for proton-antiproton elastic scattering at collider and tevatron energies

International Nuclear Information System (INIS)

Aleem, Fazal; Saleem, Mohammad

1988-01-01

The Regge pole plus cut model has been used to explain the data at the collider energies √=546 and 630 GeV and the most recent differential cross-section results at √=1.8 TeV. Predictions of the model at 1.8 and 40 TeV are compared with those of Bourrely et al. (1984). (author). 22 refs., 7 figs

Series expansion in fractional calculus and fractional differential equations

OpenAIRE

Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao

2009-01-01

Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this theorem, in this paper we introduce fractional series expansion method to fractional calculus. We define a kind of fractional Taylor series of an infinitely fractionally-differentiable function. Further, based on our definition we generalize hypergeometric functio...

A direct extension of Meller's calculus

Directory of Open Access Journals (Sweden)

E. L. Koh

1982-01-01

Full Text Available This paper extends the operational calculus of Meller for the operator Bα=t−αddttα+1ddt to the case where α∈(0,∞. The development is àla Mikusinski calculus and uses Meller's convolution process with a fractional derivative operator.

Advanced calculus of a single variable

CERN Document Server

Geveci, Tunc

2016-01-01

This advanced undergraduate textbook is based on a one-semester course on single variable calculus that the author has been teaching at San Diego State University for many years. The aim of this classroom-tested book is to deliver a rigorous discussion of the concepts and theorems that are dealt with informally in the first two semesters of a beginning calculus course. As such, students are expected to gain a deeper understanding of the fundamental concepts of calculus, such as limits (with an emphasis on ε-δ definitions), continuity (including an appreciation of the difference between mere pointwise and uniform continuity), the derivative (with rigorous proofs of various versions of L’Hôpital’s rule) and the Riemann integral (discussing improper integrals in-depth, including the comparison and Dirichlet tests). Success in this course is expected to prepare students for more advanced courses in real and complex analysis and this book will help to accomplish this. The first semester of advanced calculus...

The Effects of Two Semesters of Secondary School Calculus on Students' First and Second Quarter Calculus Grades at the University of Utah

Science.gov (United States)

Robinson, William Baker

1970-01-01

The predicted and actual achievement in college calculus is compared for students who had studied two semesters of calculus in high school. The regression equation used for prediction was calculated from the performance data of similar students who had not had high school calculus. (CT)

Computer Managed Instruction Homework Modules for Calculus I.

Science.gov (United States)

Goodman-Petrushka, Sharon; Roitberg, Yael

This booklet contains 11 modules (290 multiple-choice items) designed for use in the first course of a three-course calculus sequence using the textbook "Calculus with Analytic Geometry" (Dennis G. Zill). In each module, relevant sections of the textbook are identified for users. It can, however, be used in conjunction with any calculus textbook.…

Renal vein thrombosis mimicking urinary calculus: a dilemma of diagnosis.

Science.gov (United States)

Wang, Yimin; Chen, Shanwen; Wang, Wei; Liu, Jianyong; Jin, Baiye

2015-07-02

Renal vein thrombosis (RVT) with flank pain, and hematuria, is often mistaken with renal colic originating from ureteric or renal calculus. Especially in young and otherwise healthy patients, clinicians are easily misled by clinical presentation and calcified RVT. A 38-year-old woman presented with flank pain and hematuria suggestive of renal calculus on ultrasound. She underwent extracorporeal shock wave lithotripsy that failed, leading to the recommendation that percutaneous lithotomy was necessary to remove the renal calculus. In preoperative view of the unusual shape of the calculus without hydronephrosis, noncontrast computed tomography was taken and demonstrated left ureteric calculus. However computed tomography angiography revealed, to our surprise, a calcified RVT that was initially thought to be a urinary calculus. This case shows that a calcified RVT might mimic a urinary calculus on conventional ultrasonography and ureteric calculus on noncontrast computed tomography. Subsequent computed tomography angiography disclosed that a calcified RVT caused the imaging findings, thus creating a potentially dangerous clinical pitfall. Hence, it is suggested that the possibility of a RVT needs to be considered in the differential diagnosis whenever one detects an uncommon shape for a urinary calculus.

Pre-calculus 1,001 practice problems for dummies

CERN Document Server

Sterling, Mary Jane; Sterling

2014-01-01

Prepare for calculus the smart way, with customizable pre-calculus practice 1,001 Pre-Calculus Practice Problems For Dummies offers 1,001 opportunities to gain confidence in your math skills. Much more than a workbook, this study aid provides pre-calculus problems ranked from easy to advanced, with detailed explanations and step-by-step solutions for each one. The companion website gives you free online access to all 1,001 practice problems and solutions, and you can track your progress and ID where you should focus your study time. Accessible on the go by smart phone, tablet, o

A Snapshot of the Calculus Classroom

Science.gov (United States)

Weathers, Tony D.; Latterell, Carmen M.

2003-01-01

Essentially a focus group to discuss textbook related issues, a meeting of calculus instructors from a wide variety of environments was convened and sponsored by McGraw Hill to provide feedback on the current state of the calculus classroom. This paper provides a description of the group's discussions.

Imagine Yourself in This Calculus Classroom

Science.gov (United States)

Bryan, Luajean

2007-01-01

The efforts to attract students to precalculus, trigonometry, and calculus classes became more successful at the author's school when projects-based classes were offered. Data collection from an untethered hot air balloon flight for calculus students was planned to maximize enrollment. The data were analyzed numerically, graphically, and…

Finite-dimensional calculus

International Nuclear Information System (INIS)

Feinsilver, Philip; Schott, Rene

2009-01-01

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement infinite terms Rota's 'finite operator calculus'.

A calculus for quality

DEFF Research Database (Denmark)

Nielson, Hanne Riis; Nielson, Flemming; Vigo, Roberto

2013-01-01

for default behaviour in case the ideal behaviour fails due to unreliable communication and thereby to increase the quality of service offered by the systems. The development is facilitated by a SAT-based robustness analysis to determine whether or not the code is vulnerable to unreliable communication......A main challenge of programming component-based software is to ensure that the components continue to behave in a reasonable manner even when communication becomes unreliable. We propose a process calculus, the Quality Calculus, for programming software components where it becomes natural to plan...

Schaum's outline of calculus

CERN Document Server

Ayres, Frank

1999-01-01

Students can gain a thorough understanding of differential and integral calculus with this powerful study tool. They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide­­--more than 104,000 copies were bought of the prior edition--­­includes problems and examples using graphing calculators.

A Giant Urethral Calculus.

Science.gov (United States)

Sigdel, G; Agarwal, A; Keshaw, B W

2014-01-01

Urethral calculi are rare forms of urolithiasis. Majority of the calculi are migratory from urinary bladder or upper urinary tract. Primary urethral calculi usually occur in presence of urethral stricture or diverticulum. In this article we report a case of a giant posterior urethral calculus measuring 7x3x2 cm in a 47 years old male. Patient presented with acute retention of urine which was preceded by burning micturition and dribbling of urine for one week. The calculus was pushed in to the bladder through the cystoscope and was removed by suprapubic cystolithotomy.

Discrete Calculus by Analogy

CERN Document Server

Izadi, F A; Bagirov, G

2009-01-01

With its origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. The topics covered here usually arise in many branches of science and technology, especially in discrete mathematics, numerical analysis, statistics and probability theory as well as in electrical engineering, but our viewpoint here is that these topics belong to a much more general realm of mathematics; namely calculus and differential equations because of the remarkable analogy of the subject to this branch of mathemati

Subleading Regge limit from a soft anomalous dimension

Science.gov (United States)

Brüser, Robin; Caron-Huot, Simon; Henn, Johannes M.

2018-04-01

Wilson lines capture important features of scattering amplitudes, for example soft effects relevant for infrared divergences, and the Regge limit. Beyond the leading power approximation, corrections to the eikonal picture have to be taken into account. In this paper, we study such corrections in a model of massive scattering amplitudes in N=4 super Yang-Mills, in the planar limit, where the mass is generated through a Higgs mechanism. Using known three-loop analytic expressions for the scattering amplitude, we find that the first power suppressed term has a very simple form, equal to a single power law. We propose that its exponent is governed by the anomalous dimension of a Wilson loop with a scalar inserted at the cusp, and we provide perturbative evidence for this proposal. We also analyze other limits of the amplitude and conjecture an exact formula for a total cross-section at high energies.

AP calculus AB & BC crash course

CERN Document Server

Rosebush, J

2012-01-01

AP Calculus AB & BC Crash Course - Gets You a Higher Advanced Placement Score in Less Time Crash Course is perfect for the time-crunched student, the last-minute studier, or anyone who wants a refresher on the subject. AP Calculus AB & BC Crash Course gives you: Targeted, Focused Review - Study Only What You Need to Know Crash Course is based on an in-depth analysis of the AP Calculus AB & BC course description outline and actual AP test questions. It covers only the information tested on the exams, so you can make the most of your valuable study time. Written by experienced math teachers, our

RAMAN-SPECTRA OF HUMAN DENTAL CALCULUS

NARCIS (Netherlands)

TSUDA, H; ARENDS, J

1993-01-01

Raman spectra of human dental calculus have been observed for the first time by use of micro-Raman spectroscopy. The spectral features of calculus were influenced easily by heating caused by laser irradiation. Therefore, the measurements were carried out at relatively low power (5 mW, 1-mu m spot

An Introductory Calculus-Based Mechanics Investigation

Science.gov (United States)

Allen, Bradley

2017-01-01

One challenge for the introductory physics teacher is incorporating calculus techniques into the laboratory setting. It can be difficult to strike a balance between presenting an experimental task for which calculus is essential and making the mathematics accessible to learners who may be apprehensive about applying it. One-dimensional kinematics…

Using Dynamic Software to Address Common College Calculus Stumbling Blocks

Science.gov (United States)

Seneres, Alice W.; Kerrigan, John A.

2014-01-01

There are specific topics in college calculus that can be major stumbling blocks for students. Having taught college calculus for four years to over a thousand students, we observed that even the students who have already taken pre-calculus or calculus during their high school careers had common misunderstandings. Students may remember a technique…

Extending Stochastic Network Calculus to Loss Analysis

Directory of Open Access Journals (Sweden)

Chao Luo

2013-01-01

Full Text Available Loss is an important parameter of Quality of Service (QoS. Though stochastic network calculus is a very useful tool for performance evaluation of computer networks, existing studies on stochastic service guarantees mainly focused on the delay and backlog. Some efforts have been made to analyse loss by deterministic network calculus, but there are few results to extend stochastic network calculus for loss analysis. In this paper, we introduce a new parameter named loss factor into stochastic network calculus and then derive the loss bound through the existing arrival curve and service curve via this parameter. We then prove that our result is suitable for the networks with multiple input flows. Simulations show the impact of buffer size, arrival traffic, and service on the loss factor.

Restricted diversity of dental calculus methanogens over five centuries, France.

Science.gov (United States)

Huynh, Hong T T; Nkamga, Vanessa D; Signoli, Michel; Tzortzis, Stéfan; Pinguet, Romuald; Audoly, Gilles; Aboudharam, Gérard; Drancourt, Michel

2016-05-11

Methanogens are acknowledged archaeal members of modern dental calculus microbiota and dental pathogen complexes. Their repertoire in ancient dental calculus is poorly known. We therefore investigated archaea in one hundred dental calculus specimens collected from individuals recovered from six archaeological sites in France dated from the 14(th) to 19(th) centuries AD. Dental calculus was demonstrated by macroscopic and cone-beam observations. In 56 calculus specimens free of PCR inhibition, PCR sequencing identified Candidatus Methanobrevibacter sp. N13 in 44.6%, Methanobrevibacter oralis in 19.6%, a new Methanomassiliicoccus luminyensis-like methanogen in 12.5%, a Candidatus Nitrososphaera evergladensis-like in one and Methanoculleus bourgensis in one specimen, respectively. One Candidatus Methanobrevibacter sp. N13 dental calculus was further documented by fluorescent in situ hybridization. The prevalence of dental calculus M. oralis was significantly lower in past populations than in modern populations (P = 0.03, Chi-square test). This investigation revealed a previously unknown repertoire of archaea found in the oral cavity of past French populations as reflected in preserved dental calculus.

Ancient DNA analysis of dental calculus.

Science.gov (United States)

Weyrich, Laura S; Dobney, Keith; Cooper, Alan

2015-02-01

Dental calculus (calcified tartar or plaque) is today widespread on modern human teeth around the world. A combination of soft starchy foods, changing acidity of the oral environment, genetic pre-disposition, and the absence of dental hygiene all lead to the build-up of microorganisms and food debris on the tooth crown, which eventually calcifies through a complex process of mineralisation. Millions of oral microbes are trapped and preserved within this mineralised matrix, including pathogens associated with the oral cavity and airways, masticated food debris, and other types of extraneous particles that enter the mouth. As a result, archaeologists and anthropologists are increasingly using ancient human dental calculus to explore broad aspects of past human diet and health. Most recently, high-throughput DNA sequencing of ancient dental calculus has provided valuable insights into the evolution of the oral microbiome and shed new light on the impacts of some of the major biocultural transitions on human health throughout history and prehistory. Here, we provide a brief historical overview of archaeological dental calculus research, and discuss the current approaches to ancient DNA sampling and sequencing. Novel applications of ancient DNA from dental calculus are discussed, highlighting the considerable scope of this new research field for evolutionary biology and modern medicine. Copyright © 2014 Elsevier Ltd. All rights reserved.

College Readiness: The Evaluation of Students Participating in the Historically Black College and University Program in Pre-Calculus and the Calculus Sequence

Science.gov (United States)

Hall, Angela Renee

2011-01-01

This investigative research focuses on the level of readiness of Science, Technology, Engineering, and Mathematics (STEM) students entering Historically Black Colleges and Universities (HBCU) in the college Calculus sequence. Calculus is a fundamental course for STEM courses. The level of readiness of the students for Calculus can very well play a…

The ZX-calculus is complete for stabilizer quantum mechanics

International Nuclear Information System (INIS)

Backens, Miriam

2014-01-01

The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics (QM), meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer QM, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations. (paper)

A critical Pomeron-s view of the total and triple-Regge inclusive cross-sections

International Nuclear Information System (INIS)

Della Selva, A.; Masperi, L.; Ungkitchanukit, A.; Roberto, V.

1977-04-01

An investigation of the total and triple Regge inclusive cross-sections is carried out using a critical pomeron in the framework of reggeon field theory with thresholds. For a model with P and the conventional P' and ω poles, the rise of the total cross-section cannot be accounted for. However, in a model with a single dual-unitarization type vacuum singularity and the ω pole, the data can be adequately described

Thematization of the Calculus Graphing Schema

Science.gov (United States)

Cooley, Laurel; Baker, Bernadette; Trigueros, Maria

2003-01-01

This article is the result of an investigation of students' conceptualizations of calculus graphing techniques after they had completed at least two semesters of calculus. The work and responses of 27 students to a series of questions that solicit information about the graphical implications of the first derivative, second derivative, continuity,…

A Cross-National Study of Calculus

Science.gov (United States)

Chai, Jun; Friedler, Louis M.; Wolff, Edward F.; Li, Jun; Rhea, Karen

2015-01-01

The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan…

Command injection attacks, continuations, and the Lambek calculus

Directory of Open Access Journals (Sweden)

Hayo Thielecke

2016-06-01

Full Text Available This paper shows connections between command injection attacks, continuations, and the Lambek calculus: certain command injections, such as the tautology attack on SQL, are shown to be a form of control effect that can be typed using the Lambek calculus, generalizing the double-negation typing of continuations. Lambek's syntactic calculus is a logic with two implicational connectives taking their arguments from the left and right, respectively. These connectives describe how strings interact with their left and right contexts when building up syntactic structures. The calculus is a form of propositional logic without structural rules, and so a forerunner of substructural logics like Linear Logic and Separation Logic.

Regge-like relation and a universal description of heavy-light systems

Energy Technology Data Exchange (ETDEWEB)

Chen, Kan; Liu, Xiang [Lanzhou University, School of Physical Science and Technology, Lanzhou (China); Lanzhou University, Research Center for Hadron and CSR Physics, Institute of Modern Physics of CAS, Lanzhou (China); Dong, Yubing [Institute of High Energy Physics, CAS, Beijing (China); Theoretical Physics Center for Science Facilities (TPCSF), CAS, Beijing (China); University of Chinese Academy of Sciences, School of Physical Sciences, Beijing (China); Lue, Qi-Fang [Institute of High Energy Physics, CAS, Beijing (China); Hunan Normal University, Synergetic Innovation Center for Quantum Effects and Applications (SICQEA), Changsha (China); Matsuki, Takayuki [Tokyo Kasei University, Tokyo (Japan); Nishina Center, RIKEN, Theoretical Research Division, Wako, Saitama (Japan)

2018-01-15

Using the Regge-like formula (M - m{sub Q}){sup 2} = πσL between hadron mass M and angular momentum L with a heavy quark mass m{sub Q} and a string tension σ, we analyze all the heavy-light systems, i.e., D/D{sub s}/B/B{sub s} mesons and charmed and bottom baryons. Numerical plots are obtained for all the heavy-light mesons of experimental data whose slope becomes nearly equal to 1/2 of that for light hadrons. Assuming that charmed and bottom baryons consist of one heavy quark and one light cluster of two light quarks (diquark), we apply the formula to all the heavy-light baryons including the recently discovered Ω{sub c} and find that these baryons experimentally measured satisfy the above formula. We predict the average mass values of B, B{sub s}, Λ{sub b}, Σ{sub c}, Ξ{sub c}, and Ω{sub c} with L = 2 to be 6.01, 6.13, 6.15, 3.05, 3.07, and 3.34 GeV, respectively. Our results on baryons suggest that these baryons can be safely regarded as heavy quark-light cluster configuration. We also find a universal description for all the heavy-light mesons as well as baryons, i.e., one unique line is enough to describe both of charmed and bottom heavy-light systems. Our results suggest that instead of mass itself, gluon flux energy is essential to obtain a linear trajectory. Our method gives a straight line for B{sub c} although the curved parent Regge trajectory was suggested before. (orig.)

Improving Student Success in Calculus: A Comparison of Four College Calculus Classes

Science.gov (United States)

Bagley, Spencer Franklin

The quality of education in science, technology, engineering, and mathematics (STEM) fields is an issue of particular educational and economic importance, and Calculus I is a linchpin course in STEM major tracks. A national study is currently being conducted examining the characteristics of successful programs in college calculus (CSPCC, 2012). In work related to the CSPCC program, this study examines the effects on student outcomes of four different teaching strategies used at a single institution. The four classes were a traditional lecture, a lecture with discussion, a lecture incorporating both discussion and technology, and an inverted model. This dissertation was guided by three questions: (1) What impact do these four instructional approaches have on students' persistence, beliefs about mathematics, and conceptual and procedural achievement in calculus? (2) How do students at the local institution compare to students in the national database? And (3) How do the similarities and differences in opportunities for learning presented in the four classes contribute to the similarities and differences in student outcomes? Quantitative analysis of surveys and exams revealed few statistically significant differences in outcomes, and students in the inverted classroom often had poorer outcomes than those in other classes. Students in the technology-enhanced class scored higher on conceptual items on the final exam than those in other classes. Comparing to the national database, local students had similar switching rates but less expert-like attitudes and beliefs about mathematics than the national average. Qualitative analysis of focus group interviews, classroom observations, and student course evaluations showed that several implementation issues, some the result of pragmatic constraints, others the result of design choice, weakened affordances provided by innovative features and shrunk the differences between classes. There were substantial differences between the

Neutrosophic Precalculus and Neutrosophic Calculus

OpenAIRE

Florentin Smarandache

2015-01-01

Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis. Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of indeterminate change. The Neutrosophic Precalculus and Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the methods used to deal with such indeterminacy. In this book, the author presents a few examples o...

Feynman's operational calculus and beyond noncommutativity and time-ordering

CERN Document Server

Johnson, George W; Nielsen, Lance

2015-01-01

This book is aimed at providing a coherent, essentially self-contained, rigorous and comprehensive abstract theory of Feynman's operational calculus for noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and time-ordering rules in his seminal 1951 paper An operator calculus having applications in quantum electrodynamics, as will be made abundantly clear in the introduction (Chapter 1) and elsewhere in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work. Hence, the second part of the main title of this book. The basic properties of the operational calculus are developed and certain algebraic and analytic properties of the operational calculus are explored. Also, the operational calculus will be seen to possess some pleasant stability properties. Furthermore, an evolution equation and a generalized integral equation obeyed by the operational calculus are discussed and connections wi...

Endoscopic vs. tactile evaluation of subgingival calculus.

Science.gov (United States)

Osborn, Joy B; Lenton, Patricia A; Lunos, Scott A; Blue, Christine M

2014-08-01

Endoscopic technology has been developed to facilitate imagery for use during diagnostic and therapeutic phases of periodontal care. The purpose of this study was to compare the level of subgingival calculus detection using a periodontal endoscope with that of conventional tactile explorer in periodontitis subjects. A convenience sample of 26 subjects with moderate periodontitis in at least 2 quadrants was recruited from the University of Minnesota School of Dentistry to undergo quadrant scaling and root planing. One quadrant from each subject was randomized for tactile calculus detection alone and the other quadrant for tactile detection plus the Perioscope ™ (Perioscopy Inc., Oakland, Cali). A calculus index on a 0 to 3 score was performed at baseline and at 2 post-scaling and root planing visits. Sites where calculus was detected at visit 1 were retreated. T-tests were used to determine within-subject differences between Perioscope™ and tactile measures, and changes in measures between visits. Significantly more calculus was detected using the Perioscope™ vs. tactile explorer for all 3 subject visits (pcalculus detection from baseline to visit 1 were statistically significant for both the Perioscope™ and tactile quadrants (pcalculus detection from visit 1 to visit 2 was only significant for the Perioscope™ quadrant (pcalculus at this visit. It was concluded that the addition of a visual component to calculus detection via the Perioscope™ was most helpful in the re-evaluation phase of periodontal therapy. Copyright © 2014 The American Dental Hygienists’ Association.

Educating about Sustainability while Enhancing Calculus

Science.gov (United States)

Pfaff, Thomas J.

2011-01-01

We give an overview of why it is important to include sustainability in mathematics classes and provide specific examples of how to do this for a calculus class. We illustrate that when students use "Excel" to fit curves to real data, fundamentally important questions about sustainability become calculus questions about those curves. (Contains 5…

Two-parameter asymptotics in magnetic Weyl calculus

International Nuclear Information System (INIS)

Lein, Max

2010-01-01

This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter ε, the case of small coupling λ to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which is prominent to obtain perturbation expansions. Three asymptotic expansions for the magnetic Weyl product of two Hoermander class symbols are proven as (i) ε<< 1 and λ<< 1, (ii) ε<< 1 and λ= 1, as well as (iii) ε= 1 and λ<< 1. Expansions (i) and (iii) are impossible to obtain with ordinary Weyl calculus. Furthermore, I relate the results derived by ordinary Weyl calculus with those obtained with magnetic Weyl calculus by one- and two-parameter expansions. To show the power and versatility of magnetic Weyl calculus, I derive the semirelativistic Pauli equation as a scaling limit from the Dirac equation up to errors of fourth order in 1/c.

Lattice gravity and strings

International Nuclear Information System (INIS)

Jevicki, A.; Ninomiya, M.

1985-01-01

We are concerned with applications of the simplicial discretization method (Regge calculus) to two-dimensional quantum gravity with emphasis on the physically relevant string model. Beginning with the discretization of gravity and matter we exhibit a discrete version of the conformal trace anomaly. Proceeding to the string problem we show how the direct approach of (finite difference) discretization based on Nambu action corresponds to unsatisfactory treatment of gravitational degrees. Based on the Regge approach we then propose a discretization corresponding to the Polyakov string. In this context we are led to a natural geometric version of the associated Liouville model and two-dimensional gravity. (orig.)

Introductory analysis a deeper view of calculus

CERN Document Server

Bagby, Richard J

2000-01-01

Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.* Written in an engaging, conversational tone and readable style while softening the rigor and theory* Takes a realistic approach to the necessary and accessible level of abstraction for the secondary education students* A thorough concentration of basic topics of calculus* Features a student-friendly introduction to delta-epsilon arguments * Includes a limited use of abstract generalizations for easy use* Covers natural logarithms and exponential functions* Provides the computational techniques often encountered in basic calculus

Calculus of tensors and differential forms

CERN Document Server

Sinha, Rajnikant

2014-01-01

Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.

The dagger lambda calculus

Directory of Open Access Journals (Sweden)

Philip Atzemoglou

2014-12-01

Full Text Available We present a novel lambda calculus that casts the categorical approach to the study of quantum protocols into the rich and well established tradition of type theory. Our construction extends the linear typed lambda calculus with a linear negation of "trivialised" De Morgan duality. Reduction is realised through explicit substitution, based on a symmetric notion of binding of global scope, with rules acting on the entire typing judgement instead of on a specific subterm. Proofs of subject reduction, confluence, strong normalisation and consistency are provided, and the language is shown to be an internal language for dagger compact categories.

Reliability of recordings of subgingival calculus detected using an ultrasonic device.

Science.gov (United States)

Corraini, Priscila; López, Rodrigo

2015-04-01

To assess the intra-examiner reliability of recordings of subgingival calculus detected using an ultrasonic device, and to investigate the influence of subject-, tooth- and site-level factors on the reliability of these subgingival calculus recordings. On two occasions, within a 1-week interval, 147 adult periodontitis patients received a full-mouth clinical periodontal examination by a single trained examiner. Duplicate subgingival calculus recordings, in six sites per tooth, were obtained using an ultrasonic device for calculus detection and removal. Agreement was observed in 65 % of the 22,584 duplicate subgingival calculus recordings, ranging 45 % to 83 % according to subject. Using hierarchical modeling, disagreements in the subgingival calculus duplicate recordings were more likely in all other sites than the mid-buccal, and in sites harboring supragingival calculus. Disagreements were less likely in sites with PD ≥  4 mm and with furcation involvement  ≥  degree 2. Bleeding on probing or suppuration did not influence the reliability of subgingival calculus. At the subject-level, disagreements were less likely in patients presenting with the highest and lowest extent categories of the covariate subgingival calculus. The reliability of subgingival calculus recordings using the ultrasound technology is reasonable. The results of the present study suggest that the reliability of subgingival calculus recordings is not influenced by the presence of inflammation. Moreover, subgingival calculus can be more reliably detected using the ultrasound device at sites with higher need for periodontal therapy, i.e., sites presenting with deep pockets and premolars and molars with furcation involvement.

Malliavin Calculus With Applications to Stochastic Partial Differential Equations

CERN Document Server

Sanz-Solé, Marta

2005-01-01

Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics.This book presents applications of Malliavin calculus to the analysis of probability laws of solutions to stochastic partial differential equations driven by Gaussian noises that are white in time and coloured in space. The first five chapters introduce the calculus itself

Mesonic and baryonic Regge trajectories with quantized masses

International Nuclear Information System (INIS)

Hothi, N.; Bisht, S.

2011-01-01

We have constructed some Regge trajectories for mesons and baryons by taking the 70 MeV spinless mass quanta as the ultimate building block for the light hadrons. In order to make masses integral multiples of seventy, small changes in masses has been made with due explanation. We have shown how a linear relationship between J and M 2 is maintained by considering quantized hadron masses, which is a direct consequence of the string model and gives a strong clue for quark confinement. It has also been established that mesons and baryons have different slopes and the slopes of baryons is less than the slope of the mesons. This clearly defies the concept of universality of slopes (α ≅ 1.1 GeV 2 ) of hadrons, which can only be achieved if the strings joining the quarks have constant string tension α 1/(2πω) (where ω is the string tension). (author)

Ostrogradski approach for the Regge-Teitelboim type cosmology

International Nuclear Information System (INIS)

Cordero, Ruben; Molgado, Alberto; Rojas, Efrain

2009-01-01

We present an alternative geometric inspired derivation of the quantum cosmology arising from a brane universe in the context of geodetic gravity. We set up the Regge-Teitelboim model to describe our universe, and we recover its original dynamics by thinking of such field theory as a second-order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. Our analysis highlights the second-order derivative nature of the RT model and the inherited geometrical aspect of the theory. A canonical transformation brings us to the internal physical geometry of the theory and induces its quantization straightforwardly. By using the Dirac canonical quantization method our approach comprises the management of both first- and second-class constraints where the counting of degrees of freedom follows accordingly. At the quantum level our Wheeler-De Witt equation agrees with previous results recently found. On these lines, we also comment upon the compatibility of our approach with the Hamiltonian approach proposed by Davidson and coworkers.

TWO-PHASE EJECTOR of CARBON DIOXIDE HEAT PUMP CALCULUS

Directory of Open Access Journals (Sweden)

Sit B.M.

2010-12-01

Full Text Available It is presented the calculus of the two-phase ejector for carbon dioxide heat pump. The method of calculus is based on the method elaborated by S.M. Kandil, W.E. Lear, S.A. Sherif, and is modified taking into account entrainment ratio as the input for the calculus.

The Complex Gradient Operator and the CR-Calculus

OpenAIRE

Kreutz-Delgado, Ken

2009-01-01

A thorough discussion and development of the calculus of real-valued functions of complex-valued vectors is given using the framework of the Wirtinger Calculus. The presented material is suitable for exposition in an introductory Electrical Engineering graduate level course on the use of complex gradients and complex Hessian matrices, and has been successfully used in teaching at UC San Diego. Going beyond the commonly encountered treatments of the first-order complex vector calculus, second-...

Coupling non-gravitational fields with simplicial spacetimes

International Nuclear Information System (INIS)

McDonald, Jonathan R; Miller, Warner A

2010-01-01

The inclusion of source terms in discrete gravity is a long-standing problem. Providing a consistent coupling of source to the lattice in the Regge calculus (RC) yields a robust unstructured spacetime mesh applicable to both numerical relativity and quantum gravity. RC provides a particularly insightful approach to this problem with its purely geometric representation of spacetime. The simplicial building blocks of RC enable us to represent all matter and fields in a coordinate-free manner. We provide an interpretation of RC as a discrete exterior calculus framework into which non-gravitational fields naturally couple with the simplicial lattice. Using this approach we obtain a consistent mapping of the continuum action for non-gravitational fields to the Regge lattice. In this paper we apply this framework to scalar, vector and tensor fields. In particular we reconstruct the lattice action for (1) the scalar field, (2) Maxwell field tensor and (3) Dirac particles. The straightforward application of our discretization techniques to these three fields demonstrates a universal implementation of the coupling source to the lattice in RC.

Noninvasive control of dental calculus removal: qualification of two fluorescence methods

Science.gov (United States)

Gonchukov, S.; Sukhinina, A.; Bakhmutov, D.; Biryukova, T.

2013-02-01

The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise noninvasive detection of calculus-tooth interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing.

Noninvasive control of dental calculus removal: qualification of two fluorescence methods

International Nuclear Information System (INIS)

Gonchukov, S; Sukhinina, A; Bakhmutov, D; Biryukova, T

2013-01-01

The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise noninvasive detection of calculus-tooth interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing.

Areas and Volumes in Pre-Calculus

Science.gov (United States)

Jarrett, Joscelyn A.

2008-01-01

This article suggests the introduction of the concepts of areas bounded by plane curves and the volumes of solids of revolution in Pre-calculus. It builds on the basic knowledge that students bring to a pre-calculus class, derives a few more formulas, and gives examples of some problems on plane areas and the volumes of solids of revolution that…

White noise calculus and Fock space

CERN Document Server

Obata, Nobuaki

1994-01-01

White Noise Calculus is a distribution theory on Gaussian space, proposed by T. Hida in 1975. This approach enables us to use pointwise defined creation and annihilation operators as well as the well-established theory of nuclear space.This self-contained monograph presents, for the first time, a systematic introduction to operator theory on fock space by means of white noise calculus. The goal is a comprehensive account of general expansion theory of Fock space operators and its applications. In particular,first order differential operators, Laplacians, rotation group, Fourier transform and their interrelations are discussed in detail w.r.t. harmonic analysis on Gaussian space. The mathematical formalism used here is based on distribution theory and functional analysis , prior knowledge of white noise calculus is not required.

Programming Language Concepts - The Lambda Calculus Approach

NARCIS (Netherlands)

Fokkinga, M.M.; Asveld, P.R.J.; Nijholt, Antinus

1987-01-01

The Lambda Calculus is a formal system, originally intended as a tool in the foundation of mathematics, but mainly used to study the concepts of algorithm and effective computability. Recently, the Lambda Calculus and related systems acquire attention from Computer Science for another reason too:

A Transition Course from Advanced Placement to College Calculus

Science.gov (United States)

Lucas, Timothy A.; Spivey, Joseph

2011-01-01

In the Spring of 2007, a group of highly motivated mathematics graduate students conducted a review of Duke's Calculus curriculum. They focused on two main problems. The first problem is the result of a very positive trend: a growing number of students are earning AP credit for Calculus I in high school. However, this results in Calculus II…

Spin-dependent structure functions of sea quarks in the framework of nonperturbative QCD and new Regge trajectory

International Nuclear Information System (INIS)

Dorokhov, A.E.; Kochelev, N.I.

1991-01-01

Within the model of QCD vacuum as an instanton liquid the spin-dependent structure functions of sea quarks are obtained. It is shown that the EMC data manages the definition of new Regge trajectory connected with the axial anomaly. The model explains the modern experimental data on the sea quark structure functions. 23 refs.; 3 figs

Everyday calculus discovering the hidden math all around us

CERN Document Server

Fernandez, Oscar E

2014-01-01

Calculus. For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. In Everyday Calculus, Oscar Fernandez shows us how to see the math in our coffee, on the highway, and even in the night sky. Fernandez uses our everyday experiences to skillfully reveal the hidden calculus behind a typical day's events. He guides us through how math naturally emerges from simple observations-how hot coffee cools down, for example-and in discussions of over fifty familia

Scale calculus and the Schroedinger equation

International Nuclear Information System (INIS)

Cresson, Jacky

2003-01-01

This paper is twofold. In a first part, we extend the classical differential calculus to continuous nondifferentiable functions by developing the notion of scale calculus. The scale calculus is based on a new approach of continuous nondifferentiable functions by constructing a one parameter family of differentiable functions f(t,ε) such that f(t,ε)→f(t) when ε goes to zero. This led to several new notions as representations: fractal functions and ε-differentiability. The basic objects of the scale calculus are left and right quantum operators and the scale operator which generalizes the classical derivative. We then discuss some algebraic properties of these operators. We define a natural bialgebra, called quantum bialgebra, associated with them. Finally, we discuss a convenient geometric object associated with our study. In a second part, we define a first quantization procedure of classical mechanics following the scale relativity theory developed by Nottale. We obtain a nonlinear Schroedinger equation via the classical Newton's equation of dynamics using the scale operator. Under special assumptions we recover the classical Schroedinger equation and we discuss the relevance of these assumptions

Towards Model Checking a Spi-Calculus Dialect

NARCIS (Netherlands)

Gnesi, S.; Latella, D.; Lenzini, Gabriele

We present a model checking framework for a spi-calculus dialect which uses a linear time temporal logic for expressing security properties. We have provided our spi-calculus dialect, called SPID, with a semantics based on labeled transition systems (LTS), where the intruder is modeled in the

On flipping first-semester calculus: a case study

Science.gov (United States)

Petrillo, Joseph

2016-05-01

High failure rates in calculus have plagued students, teachers, and administrators for decades, while science, technology, engineering, and mathematics programmes continue to suffer from low enrollments and high attrition. In an effort to affect this reality, some educators are 'flipping' (or inverting) their classrooms. By flipping, we mean administering course content outside of the classroom and replacing the traditional in-class lectures with discussion, practice, group work, and other elements of active learning. This paper presents the major results from a three-year study of a flipped, first-semester calculus course at a small, comprehensive, American university with a well-known engineering programme. The data we have collected help quantify the positive and substantial effects of our flipped calculus course on failure rates, scores on the common final exam, student opinion of calculus, teacher impact on measurable outcomes, and success in second-semester calculus. While flipping may not be suitable for every teacher, every student, and in every situation, this report provides some evidence that it may be a viable option for those seeking an alternative to the traditional lecture model.

Introduction to Differential Calculus Systematic Studies with Engineering Applications for Beginners

CERN Document Server

Rohde, Ulrich L; Poddar, Ajay K; Ghosh, A K

2011-01-01

Enables readers to apply the fundamentals of differential calculus to solve real-life problems in engineering and the physical sciences Introduction to Differential Calculus fully engages readers by presenting the fundamental theories and methods of differential calculus and then showcasing how the discussed concepts can be applied to real-world problems in engineering and the physical sciences. With its easy-to-follow style and accessible explanations, the book sets a solid foundation before advancing to specific calculus methods, demonstrating the connections between differential calculus

Regge behaviour of structure function and gluon distribution at low-x in leading order

International Nuclear Information System (INIS)

Sarma, J.K.

2000-01-01

We present a method to find the gluon distribution from the F 2 proton structure function data at low-x assuming the Regge behaviour of the gluon distribution function at this limit. We use the leading order (LO) Altarelli-Parisi (AP) evolution equation in our analysis and compare our result with those of other authors. We also discuss the limitations of the Taylor expansion method in extracting the gluon distribution from the F 2 structure function used by those authors. (orig.)

Science 101: How Do We Use Calculus in Science?

Science.gov (United States)

Robertson, Bill

2014-01-01

How is calculus used in science? That might seem like an odd question to answer in a magazine intended primarily for elementary school teachers. After all, how much calculus gets used in elementary science? Here the author guesses that quite a few readers of this column do not know a whole lot about calculus and have not taken a course in…

Elementary calculus an infinitesimal approach

CERN Document Server

Keisler, H Jerome

2012-01-01

This first-year calculus book is centered around the use of infinitesimals, an approach largely neglected until recently for reasons of mathematical rigor. It exposes students to the intuition that originally led to the calculus, simplifying their grasp of the central concepts of derivatives and integrals. The author also teaches the traditional approach, giving students the benefits of both methods.Chapters 1 through 4 employ infinitesimals to quickly develop the basic concepts of derivatives, continuity, and integrals. Chapter 5 introduces the traditional limit concept, using approximation p

Hybrid Logical Analyses of the Ambient Calculus

DEFF Research Database (Denmark)

Bolander, Thomas; Hansen, Rene Rydhof

2010-01-01

In this paper, hybrid logic is used to formulate three control flow analyses for Mobile Ambients, a process calculus designed for modelling mobility. We show that hybrid logic is very well-suited to express the semantic structure of the ambient calculus and how features of hybrid logic can...

Fluorescence-based calculus detection using a 405-nm excitation wavelength

Science.gov (United States)

Brede, O.; Schelle, F.; Krueger, S.; Oehme, B.; Dehn, C.; Frentzen, M.; Braun, A.

2011-03-01

The aim of this study was to assess the difference of fluorescence signals of cement and calculus using a 405 nm excitation wavelength. A total number of 20 freshly extracted teeth was used. The light source used for this study was a blue LED with a wavelength of 405nm. For each tooth the spectra of calculus and cementum were measured separately. Fluorescence light was collimated into an optical fibre and spectrally analyzed using an echelle spectrometer (aryelle 200, Lasertechnik Berlin, Germany) with an additionally bandpass (fgb 67, Edmund Industrial Optics, Karlsruhe, Germany). From these 40 measurements the median values were calculated over the whole spectrum, leading to two different median spectra, one for calculus and one for cementum. For further statistical analysis we defined 8 areas of interest (AOI) in wavelength regions, showing remarkable differences in signal strength. In 7 AOIs the intensity of the calculus spectrum differed statistically significant from the intensity of the cementum spectrum (p calculus and cement between 600nm and 700nm. Thus, we can conclude that fluorescence of calculus shows a significant difference to the fluorescence of cement. A differentiation over the intensity is possible as well as over the spectrum. Using a wavelength of 405nm, it is possible to distinguish between calculus and cement. These results could be used for further devices to develop a method for feedback controlled calculus removal.

Subgingival calculus imaging based on swept-source optical coherence tomography

Science.gov (United States)

Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Lu, Chih-Wei; Jiang, Cho-Pei; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei

2011-07-01

We characterized and imaged dental calculus using swept-source optical coherence tomography (SS-OCT). The refractive indices of enamel, dentin, cementum, and calculus were measured as 1.625 +/- 0.024, 1.534 +/- 0.029, 1.570 +/- 0.021, and 2.097 +/- 0.094, respectively. Dental calculus leads strong scattering properties, and thus, the region can be identified from enamel with SS-OCT imaging. An extracted human tooth with calculus is covered with gingiva tissue as an in vitro sample for tomographic imaging.

On the role of individualized Regge poles in forming refractive structures in light and heavy ion scattering at large angles

International Nuclear Information System (INIS)

Kuznichenko, A.V.; Onyshchenko, G.M.; Pilipenko, V.V.; Burtebaev, N.; Zhurunbayeva, G.S.

2002-01-01

Investigation of the refraction structures in cross sections of nuclear scattering is a well-known method of probing the interior parts of the interaction region of colliding nuclei and attracts much attention. During recent years essential success was achieved in the experimental studies of scattering of light and heavy ions in wide scattering angle range. The studies were carried out not only in the energy region with standard nuclear rainbow behavior but also at energies near and below the critical energy of nuclear rainbow E cr which revealed well pronounced refractive structures in the angular distributions of the processes studied including rainbow-like maximums and anomalous large angle scattering. To analyze evolution of the refraction effects with energy a new S-matrix model, which can supplement the results of the analyses on the basis of commonly used optical potential approach. The S-matrix model takes into account of some Regge poles near the real axis ('individualized' poles), which addresses the case of energies near and below E cr . Basing on developed model a number a scattering patterns for system α+A, 16 O+ 16 O and 16 O+ 12 C at different energy values have been analyzed. The comparison with results of optical model analyses have been made. The studies were complemented by the analysis on basis of the modified Fuller procedure of decomposition of cross sections into near and far components with removing unphysical contributions. The results of analysis performed suggest the conclusion that the observed refractive structures at large angles (both the rainbow-like ones and ALAS) at E≤E cr are strongly affected by the above mentioned individualized Regge poles. Strictly saying, the scattering in this energy region is not a pure rainbow one, but is of transition character. The arising Regge poles can be considered as a quantum analog for the transition to the orbiting regime in the case of classical scattering. The notch test of the sensitivity

Calculator calculus

CERN Document Server

McCarty, George

1982-01-01

How THIS BOOK DIFFERS This book is about the calculus. What distinguishes it, however, from other books is that it uses the pocket calculator to illustrate the theory. A computation that requires hours of labor when done by hand with tables is quite inappropriate as an example or exercise in a beginning calculus course. But that same computation can become a delicate illustration of the theory when the student does it in seconds on his calculator. t Furthermore, the student's own personal involvement and easy accomplishment give hi~ reassurance and en­ couragement. The machine is like a microscope, and its magnification is a hundred millionfold. We shall be interested in limits, and no stage of numerical approximation proves anything about the limit. However, the derivative of fex) = 67.SgX, for instance, acquires real meaning when a student first appreciates its values as numbers, as limits of 10 100 1000 t A quick example is 1.1 , 1.01 , 1.001 , •••• Another example is t = 0.1, 0.01, in the functio...

Renal calculus

CERN Document Server

Pyrah, Leslie N

1979-01-01

Stone in the urinary tract has fascinated the medical profession from the earliest times and has played an important part in the development of surgery. The earliest major planned operations were for the removal of vesical calculus; renal and ureteric calculi provided the first stimulus for the radiological investigation of the viscera, and the biochemical investigation of the causes of calculus formation has been the training ground for surgeons interested in metabolic disorders. It is therefore no surprise that stone has been the subject of a number of monographs by eminent urologists, but the rapid development of knowledge has made it possible for each one of these authors to produce something new. There is still a technical challenge to the surgeon in the removal of renal calculi, and on this topic we are always glad to have the advice of a master craftsman; but inevitably much of the interest centres on the elucidation of the causes of stone formation and its prevention. Professor Pyrah has had a long an...

Intitialization, Conceptualization, and Application in the Generalized Fractional Calculus

Science.gov (United States)

Lorenzo, Carl F.; Hartley, Tom T.

1998-01-01

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.

Initialization, conceptualization, and application in the generalized (fractional) calculus.

Science.gov (United States)

Lorenzo, Carl F; Hartley, Tom T

2007-01-01

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.

Calculus in High School--At What Cost?

Science.gov (United States)

Sorge, D. H.; Wheatley, G. H.

1977-01-01

Evidence on the decline in preparation of entering calculus students and the relationship to high school preparation is presented, focusing on the trend toward the de-emphasis of trigonometry and analytic geometry in favor of calculus. Data on students' perception of the adequacy of their preparation are also presented. (Author/MN)

Calculus and Success in a Business School

Science.gov (United States)

Kim, Dong-gook; Garcia, Fernando; Dey, Ishita

2012-01-01

Many business schools or colleges require calculus as a prerequisite for certain classes or for continuing to upper division courses. While there are many studies investigating the relationship between performance in calculus and performance in a single course, such as economics, statistics, and finance, there are very few studies investigating…

Generalized Cartan Calculus in general dimension

Science.gov (United States)

Wang, Yi-Nan

2015-07-01

We develop the generalized Cartan Calculus for the groups and SO(5 , 5). They are the underlying algebraic structures of d = 9 , 7 , 6 exceptional field theory, respectively. These algebraic identities are needed for the "tensor hierarchy" structure in exceptional field theory. The validity of Poincaré lemmas in this new differential geometry is also discussed. Finally we explore some possible extension of the generalized Cartan calculus beyond the exceptional series.

Superconformal tensor calculus in five dimensions

International Nuclear Information System (INIS)

Fujita, Tomoyuki; Ohashi, Keisuke

2001-01-01

We present a full superconformal tensor calculus in five spacetime dimensions in which the Weyl multiplet has 32 Bose plus 32 Fermi degrees of freedom. It is derived using dimensional reduction from the 6D superconformal tensor calculus. We present two types of 32+32 Weyl multiplets, a vector multiplet, linear multiplet, hypermultiplet and nonlinear multiplet. Their superconformal transformation laws and the embedding and invariant action formulas are given. (author)

Teaching and learning of pre-calculus: an insights of educators ...

African Journals Online (AJOL)

The high-failure of Calculus courses has bring dilemma to the educators worldwide. This study has focus on teaching and learning of Pre-Calculus, a fundamental course for higher level Calculus courses. A well-designed questionnaire was distributed to all respondents to find the difficulties faced by both lecturers and ...

Backpropagation and ordered derivatives in the time scales calculus.

Science.gov (United States)

Seiffertt, John; Wunsch, Donald C

2010-08-01

Backpropagation is the most widely used neural network learning technique. It is based on the mathematical notion of an ordered derivative. In this paper, we present a formulation of ordered derivatives and the backpropagation training algorithm using the important emerging area of mathematics known as the time scales calculus. This calculus, with its potential for application to a wide variety of inter-disciplinary problems, is becoming a key area of mathematics. It is capable of unifying continuous and discrete analysis within one coherent theoretical framework. Using this calculus, we present here a generalization of backpropagation which is appropriate for cases beyond the specifically continuous or discrete. We develop a new multivariate chain rule of this calculus, define ordered derivatives on time scales, prove a key theorem about them, and derive the backpropagation weight update equations for a feedforward multilayer neural network architecture. By drawing together the time scales calculus and the area of neural network learning, we present the first connection of two major fields of research.

Water content contribution in calculus phantom ablation during Q-switched Tm:YAG laser lithotripsy.

Science.gov (United States)

Zhang, Jian J; Rajabhandharaks, Danop; Xuan, Jason Rongwei; Wang, Hui; Chia, Ray W J; Hasenberg, Tom; Kang, Hyun Wook

2015-01-01

Q-switched (QS) Tm:YAG laser ablation mechanisms on urinary calculi are still unclear to researchers. Here, dependence of water content in calculus phantom on calculus ablation performance was investigated. White gypsum cement was used as a calculus phantom model. The calculus phantoms were ablated by a total 3-J laser pulse exposure (20 mJ, 100 Hz, 1.5 s) and contact mode with N=15 sample size. Ablation volume was obtained on average 0.079, 0.122, and 0.391  mm3 in dry calculus in air, wet calculus in air, and wet calculus in-water groups, respectively. There were three proposed ablation mechanisms that could explain the effect of water content in calculus phantom on calculus ablation performance, including shock wave due to laser pulse injection and bubble collapse, spallation, and microexplosion. Increased absorption coefficient of wet calculus can cause stronger spallation process compared with that caused by dry calculus; as a result, higher calculus ablation was observed in both wet calculus in air and wet calculus in water. The test result also indicates that the shock waves generated by short laser pulse under the in-water condition have great impact on the ablation volume by Tm:YAG QS laser.

Supergravity tensor calculus in 5D from 6D

International Nuclear Information System (INIS)

Kugo, Taichiro; Ohashi, Keisuke

2000-01-01

Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d=6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus retains the dilatation gauge symmetry, so that it is a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system. (author)

The Enriched Effect Calculus: Syntax and Semantics

DEFF Research Database (Denmark)

Møgelberg, Rasmus Ejlers; Simpson, Alex; Egger, Jeff

2014-01-01

This article introduces the enriched effect calculus, which extends established type theories for computational effects with primitives from linear logic. The new calculus provides a formalism for expressing linear aspects of computational effects; e.g. the linear usage of imperative features....... The second half of the article investigates models for the enriched effect calculus, based on enriched category theory. We give several examples of such models, relating them to models of standard effect calculi (such as those based on monads), and to models of intuitionistic linear logic. We also prove...

On the Expressive Power of Polyadic Synchronisation in Pi-Calculus

DEFF Research Database (Denmark)

Carbone, Marco; Maffeis, Sergio

2003-01-01

We extend the π-calculus with polyadic synchronisation, a generalisation of the communication mechanism which allows channel names to be composite. We show that this operator embeds nicely in the theory of π-calculus, we suggest that it permits divergence-free encodings of distributed calculi......, and we show that a limited form of polyadic synchronisation can be encoded weakly in π-calculus. After showing that matching cannot be derived in π-calculus, we compare the expressivity of polyadic synchronisation, mixed choice and matching. In particular we show that the degree of synchronisation...

Discrete Calculus as a Bridge between Scales

Science.gov (United States)

Degiuli, Eric; McElwaine, Jim

2012-02-01

Understanding how continuum descriptions of disordered media emerge from the microscopic scale is a fundamental challenge in condensed matter physics. In many systems, it is necessary to coarse-grain balance equations at the microscopic scale to obtain macroscopic equations. We report development of an exact, discrete calculus, which allows identification of discrete microscopic equations with their continuum equivalent [1]. This allows the application of powerful techniques of calculus, such as the Helmholtz decomposition, the Divergence Theorem, and Stokes' Theorem. We illustrate our results with granular materials. In particular, we show how Newton's laws for a single grain reproduce their continuum equivalent in the calculus. This allows introduction of a discrete Airy stress function, exactly as in the continuum. As an application of the formalism, we show how these results give the natural mean-field variation of discrete quantities, in agreement with numerical simulations. The discrete calculus thus acts as a bridge between discrete microscale quantities and continuous macroscale quantities. [4pt] [1] E. DeGiuli & J. McElwaine, PRE 2011. doi: 10.1103/PhysRevE.84.041310

A calculus for attribute-based communication

DEFF Research Database (Denmark)

Alrahman, Yehia Abd; De Nicola, Rocco; Loreti, Michele

2015-01-01

The notion of attribute-based communication seems promising to model and analyse systems with huge numbers of interacting components that dynamically adjust and combine their behaviour to achieve specific goals. A basic process calculus, named AbC, is introduced that has as primitive construct...... of how well-established process calculi could be encoded into AbC is given by considering the translation into AbC of a proto-typical π-calculus process....

The impacts of gingivitis and calculus on Thai children's quality of life.

Science.gov (United States)

Krisdapong, Sudaduang; Prasertsom, Piyada; Rattanarangsima, Khanit; Sheiham, Aubrey; Tsakos, Georgios

2012-09-01

To assess associations of socio-demographic, behavioural and the extent of gingivitis and calculus with oral health-related quality of life (OHRQoL) in nationally representative samples of 12- and 15-year-old Thai children. In the Thailand National Oral Health Survey, 1,063 twelve-year olds and 811 fifteen-year olds were clinically examined and interviewed for OHRQoL using the Child-OIDP and OIDP indices, respectively, and completed a behavioural questionnaire. We assessed associations of condition-specific impacts (CS-impacts) with gingivitis and calculus, adjusted for socio-demographic and behavioural factors. Gingivitis and calculus were highly prevalent: 79.3% in 12-year and 81.5% in 15-year olds. CS-impacts relating to calculus and/or gingivitis were reported by 26.0% of 12-year and 29.6% of 15-year olds. Except for calculus without gingivitis, calculus and/or gingivitis in any form was significantly related to any level of CS-impacts. At a moderate or higher level of CS-impacts, there were significant relationships with extensive calculus and/or gingivitis in 12-year olds and for extensive gingivitis and gingivitis without calculus in 15-year olds. Gingivitis was generally associated with any level of CS-impacts attributed to calculus and/or gingivitis. CS-impacts were related more to gingivitis than to calculus. © 2012 John Wiley & Sons A/S.

Giant Calculus In The Mouth Of Partially Edentulous Woman, (Case ...

African Journals Online (AJOL)

Objective: This case report is to create awareness of the presence of giant calculus in the mouth, the possible causes and its prevention. Report: This describes the oral condition of a partially edentulous woman with a giant calculus in the mouth. It highlights the effect of such an enormous calculus in the oral cavity.

Improving Calculus II and III through the Redistribution of Topics

Science.gov (United States)

George, C. Yousuf; Koetz, Matt; Lewis, Heather A.

2016-01-01

Three years ago our mathematics department rearranged the topics in second and third semester calculus, moving multivariable calculus to the second semester and series to the third semester. This paper describes the new arrangement of topics, and how it could be adapted to calculus curricula at different schools. It also explains the benefits we…

The Bethe roots of Regge cuts in strongly coupled N=4 SYM theory

International Nuclear Information System (INIS)

Bartels, J.; Schomerus, V.; Sprenger, M.

2015-01-01

We describe a general algorithm for the computation of the remainder function for n-gluon scattering in multi-Regge kinematics for strongly coupled planar N=4 super Yang-Mills theory. This regime is accessible through the infrared physics of an auxiliary quantum integrable system describing strings in AdS 5 ×S 5 . Explicit formulas are presented for n=6 and n=7 external gluons. Our results are consistent with expectations from perturbative gauge theory. This paper comprises the technical details for the results announced in http://dx.doi.org/10.1007/JHEP10(2014)067.

Fractional calculus in bioengineering, part 3.

Science.gov (United States)

Magin, Richard L

2004-01-01

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub

Partial Fractions in Calculus, Number Theory, and Algebra

Science.gov (United States)

Yackel, C. A.; Denny, J. K.

2007-01-01

This paper explores the development of the method of partial fraction decomposition from elementary number theory through calculus to its abstraction in modern algebra. This unusual perspective makes the topic accessible and relevant to readers from high school through seasoned calculus instructors.

Application of a Regge model to the photoproduction of pion pairs

Energy Technology Data Exchange (ETDEWEB)

Bolz, Arthur; Sauter, Michel; Schoening, Andre [Physikalisches Institut, Universitaet Heidelberg, Im Neuenheimer Feld 226, D-69120 Heidelberg (Germany); Ewerz, Carlo [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany); ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum fuer Schwerionenforschung, Planckstrasse 1, D-64291 Darmstadt (Germany); Maniatis, Markos [Departamento de Ciencias Basicas, Universidad del Bio-Bio, Avda. Andres Bello s/n, Casilla 447, Chillan 3780000 (Chile); Nachtmann, Otto [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)

2015-07-01

In a recent publication (arXiv:1409.8483) a model in the spirit of Regge theory is used to describe the reaction γp → π{sup +}π{sup -} p at high energies. Both resonant pion-pion production via the meson resonances ρ(770), ω(782), ρ(1450) and f{sub 2}(1270) as well as non-resonant amplitudes are considered. Photon and proton interact by the exchange of the photon, the pomeron and reggeons as well as by a yet unobserved but possible odderon. Cross sections calculated from this model and their dependencies on various kinematic quantities are discussed and compared to experimental data. The focus is on angular distributions which feature asymmetries that could be used for an odderon discovery.

Understanding Calculus beyond Computations: A Descriptive Study of the Parallel Meanings and Expectations of Teachers and Users of Calculus

Science.gov (United States)

Ferguson, Leann J.

2012-01-01

Calculus is an important tool for building mathematical models of the world around us and is thus used in a variety of disciplines, such as physics and engineering. These disciplines rely on calculus courses to provide the mathematical foundation needed for success in their courses. Unfortunately, due to the basal conceptions of what it means to…

Thunks and the λ-calculus

DEFF Research Database (Denmark)

Hatcliff, John; Danvy, Olivier

1997-01-01

Thirty-five years ago, thunks were used to simulate call-by-name under call-by-value in Algol 60. Twenty years ago, Plotkin presented continuation-based simulations of call-by-name under call-by-value and vice versa in the λ-calculus. We connect all three of these classical simulations by factori......Thirty-five years ago, thunks were used to simulate call-by-name under call-by-value in Algol 60. Twenty years ago, Plotkin presented continuation-based simulations of call-by-name under call-by-value and vice versa in the λ-calculus. We connect all three of these classical simulations...

Quantum mechanics and umbral calculus

International Nuclear Information System (INIS)

Lopez-Sendino, J E; Negro, J; Olmo, M A del; Salgado, E

2008-01-01

In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones and the space-time continuous variables by well determined operators that verify some Umbral Calculus conditions. In this way we assure that some properties of integrability and symmetries of the continuous equation are preserved and also the solutions of the continuous case can be recovered discretized in a simple way. The case of the Schroedinger equation with a potential depending only in the space variable is discussed.

A Graph Calculus for Predicate Logic

Directory of Open Access Journals (Sweden)

Paulo A. S. Veloso

2013-03-01

Full Text Available We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents bottom. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we can recognize conflicting situations (equivalent to a formula and its negation.

Sandboxing in a Distributed Pi-Calculus

DEFF Research Database (Denmark)

Hüttel, Hans; Kühnrich, Morten

2006-01-01

This paper presents an extension of the Dpi-calculus due to Hennessy and Riely with constructs for signing and authenticating code and for sandboxing. A sort system, built on Milner's sort systems for the polyadic pi-calculus, is presented and proven sound with respect to an error predicate which...... ensures that errors do not occur outside sandboxes and that authentication and migration only happen when allowed. Futhermore a weak subject reduction result involving partial well sortedness is presented....

A MATLAB companion for multivariable calculus

CERN Document Server

Cooper, Jeffery

2001-01-01

Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, A MatLab Companion for Multivariable Calculus introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton''s method in several variables, thereby allowing students to tackle realistic problems. The many examples show students how to use MatLab effectively and easily in many contexts. Numerous exercises in mathematics and applications areas are presented, graded from routine to more demanding projects requiring some programming. Matlab M-files are provided on the Harcourt/Academic Press web site at http://www.harcourt-ap.com/matlab.html.* Computer-oriented material that complements the essential topics in multivariable calculus* Main ideas presented with examples of computations and graphics displays using MATLAB * Numerous examples of short code in the text, which can be modified for use with the exercises* MATLAB files are used to implem...

The dental calculus metabolome in modern and historic samples

DEFF Research Database (Denmark)

Velsko, Irina M.; Overmyer, Katherine A.; Speller, Camilla

2017-01-01

Introduction: Dental calculus is a mineralized microbial dental plaque biofilm that forms throughout life by precipitation of salivary calcium salts. Successive cycles of dental plaque growth and calcification make it an unusually well-preserved, long-term record of host-microbial interaction...... in the archaeological record. Recent studies have confirmed the survival of authentic ancient DNA and proteins within historic and prehistoric dental calculus, making it a promising substrate for investigating oral microbiome evolution via direct measurement and comparison of modern and ancient specimens. Objective: We...... present the first comprehensive characterization of the human dental calculus metabolome using a multi-platform approach. Methods: Ultra performance liquid chromatography-tandem mass spectrometry (UPLC–MS/MS) quantified 285 metabolites in modern and historic (200 years old) dental calculus, including...

Equality and fixpoints in the calculus of structures

DEFF Research Database (Denmark)

Chaudhuri, Kaustuv; Guenot, Nicolas

2014-01-01

The standard proof theory for logics with equality and fixpoints suffers from limitations of the sequent calculus, where reasoning is separated from computational tasks such as unification or rewriting. We propose in this paper an extension of the calculus of structures, a deep inference formalism...

Quantum stochastic calculus and representations of Lie superalgebras

CERN Document Server

Eyre, Timothy M W

1998-01-01

This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson-Parthasarathy quantum stochastic calculus. Quantum stochastic calculus and grading theory are given concise introductions, extending readership to mathematicians and physicists with a basic knowledge of algebra and infinite-dimensional Hilbert spaces. The develpment of an explicit formula for the chaotic expansion of a polynomial of quantum stochastic integrals is particularly interesting. The book aims to provide a self-contained exposition of what is known about Z_2-graded quantum stochastic calculus and to provide a framework for future research into this new and fertile area.

On the Lipschitz condition in the fractal calculus

International Nuclear Information System (INIS)

Golmankhaneh, Alireza K.; Tunc, Cemil

2017-01-01

In this paper, the existence and uniqueness theorems are proved for the linear and non-linear fractal differential equations. The fractal Lipschitz condition is given on the F"α-calculus which applies for the non-differentiable function in the sense of the standard calculus. More, the metric spaces associated with fractal sets and about functions with fractal supports are defined to build fractal Cauchy sequence. Furthermore, Picard iterative process in the F"α-calculus which have important role in the numerical and approximate solution of fractal differential equations is explored. We clarify the results using the illustrative examples.

The absolute differential calculus calculus of tensors

CERN Document Server

Levi-Cività, Tullio

1926-01-01

Written by a towering figure of twentieth-century mathematics, this classic examines the mathematical background necessary for a grasp of relativity theory. Tullio Levi-Civita provides a thorough treatment of the introductory theories that form the basis for discussions of fundamental quadratic forms and absolute differential calculus, and he further explores physical applications.Part one opens with considerations of functional determinants and matrices, advancing to systems of total differential equations, linear partial differential equations, algebraic foundations, and a geometrical intro

Covariant differential calculus on the quantum hyperplane

International Nuclear Information System (INIS)

Wess, J.

1991-01-01

We develop a differential calculus on the quantum hyperplane covariant with respect to the action of the quantum group GL q (n). This is a concrete example of noncommutative differential geometry. We describe the general constraints for a noncommutative differential calculus and verify that the example given here satisfies all these constraints. We also discuss briefly the integration over the quantum plane. (orig.)

Regge vertex for quark production in the central rapidity region in the next-to-leading order

Energy Technology Data Exchange (ETDEWEB)

Kozlov, M. G., E-mail: M.G.Kozlov@inp.nsk.su; Reznichenko, A. V., E-mail: A.V.Reznichenko@inp.nsk.su [Russian Academy of Sciences, Budker Institute of Nuclear Physics, Siberian Branch (Russian Federation)

2016-03-15

The effective vertex for quark production in the interaction of a Reggeized quark and a Reggeized gluon is calculated in the next-to-leading order (NLO). The resulting vertex is the missing component of the NLO multi-Regge amplitude featuring quark and gluon exchanges in the t channels. This calculation will make it possible to develop in future the bootstrap approach to proving quark Reggeization in the next-to-leading logarithmic approximation.

Many-hadron production at low Psub(perpendicular)

Energy Technology Data Exchange (ETDEWEB)

Bassetto, A [Dipartimento di Matematica e Fisica della Libera Universita di Trento, Trento (Italy); Istituto Nazionale di Fisica Nucleare, Padua (Italy))

1978-01-01

Different pictures of many-body particle production are reviewed. Two different and, in a sense, complementary approaches are examined: the multiperipheral approach with its natural continuation in the Gribov-Regge calculus and the jet models. Rather than being exhaustive the author tries to point out some aspects and collect some ideas which might be useful for a possible future theory.

Fractional vector calculus and fractional Maxwell's equations

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2008-01-01

The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered

The giant calculus within the prostatic urethra.

Science.gov (United States)

Demir, Omer; Kefi, Aykut; Cahangirov, Asif; Cihan, Ahmet; Obuz, Funda; Esen, Adil Ahmet; Celebi, Ilhan

2011-08-01

The giant calculus within the prostatic urethra is a rare clinical entity in the young population. Most of the calculi within the urethra migrate from the urinary bladder and obliterate the urethra. These stones are often composed of calcium phosphate or calcium oxalate. The decision of treatment strategy is affected by the size, shape and position of the calculus and by the status of the urethra. If the stone is large and immovable, it may be extracted via the perineal or the suprapubic approach. In most cases, the giant calculi were extracted via the transvesical approach and external urethrotomy. Our case is the biggest prostatic calculus, known in the literature so far, which was treated endoscopically by the combination of laser and the pneumatic lithotriptor.

Reggeon, Pomeron and Glueball, Odderon-Hadron-Hadron Interaction at High Energies--From Regge Theory to Quantum Chromodynamics

Institute of Scientific and Technical Information of China (English)

XIONG Wen-Yuan; HU Zhao-Hui; WANG Xin-Wen; ZHOU Li-Juan; XIA Li-Xin; MA Wei-Xing

2008-01-01

Based on analysis of scattering matrix S, and its properties such as analyticity, unitarity, Lorentz invariance, and crossing symmetry relation, the Regge theory was proposed to describe hadron-hadron scattering at high energies before the advent of QCD, and correspondingly a Reggeon concept was born as a mediator of strongly interaction. This theory serves as a successful approach and has explained a great number of experimental data successfully, which proves that the Regge theory can be regarded as a basic theory of hadron interaction at high energies and its validity in many applications. However, as new experimental data come out, we have some difficulties in explaining the data. The new experimental total cross section violates the predictions of Regge theory, which shows that Regge formalism is limited in its applications to high energy data. To understand new experimental measurements, a new exchange theory was consequently born and its mediator is called Pomeron, which has vacuum quantum numbers. The new theory named as Pomeron exchange theory which reproduces the new experimental data of diffractive processes successfully. There are two exchange mediators: Reggeon and Pomeron. Reggeon exchange theory can only produce data at the relatively lower energy region, while Pomeron exchange theory fits the data only at higher-energy region, separately. In order to explain the data in the whole energy region, we propose a Reggeon-Pomeron model to describe high-energy hadron-hadron scattering and other diffractive processes. Although the Reggeon-Pomeron model is successful in describing high-energy hadron-hadron interaction in the whole energy region, it is a phenomenological model After the advent of QCD, people try to reveal the mystery of the phenomenological theory from QCD since hadron-hadron processes is a strong interaction, which is believed to be described by QCD. According to this point of view, we study the QCD nature of Reggeon and Pomeron. We claim

Calculus Instructors' and Students' Discourses on the Derivative

Science.gov (United States)

Park, Jungeun

2011-01-01

Recently, there has been an increasing interest in collegiate mathematics education, especially teaching and learning calculus (e.g., Oehrtman, Carlson, & Thompson, 2008; Speer, Smith, & Horvath, 2010). Of many calculus concepts, the derivative is known as a difficult concept for students to understand because it involves various concepts…

Reflections on Our First Calculus Undergraduate Teaching Assistant

Science.gov (United States)

Deshler, Jessica M.

2016-01-01

This article describes some reflections from the first Calculus I undergraduate teaching assistant in our department as she explored the various ways in which she was able to support both novice and experienced Calculus teachers and the effect of her experience on her academic and career plans.

Executable Behaviour and the π-Calculus (extended abstract

Directory of Open Access Journals (Sweden)

Bas Luttik

2015-08-01

Full Text Available Reactive Turing machines extend classical Turing machines with a facility to model observable interactive behaviour. We call a behaviour executable if, and only if, it is behaviourally equivalent to the behaviour of a reactive Turing machine. In this paper, we study the relationship between executable behaviour and behaviour that can be specified in the pi-calculus. We establish that all executable behaviour can be specified in the pi-calculus up to divergence-preserving branching bisimilarity. The converse, however, is not true due to (intended limitations of the model of reactive Turing machines. That is, the pi-calculus allows the specification of behaviour that is not executable up to divergence-preserving branching bisimilarity. Motivated by an intuitive understanding of executability, we then consider a restriction on the operational semantics of the pi-calculus that does associate with every pi-term executable behaviour, at least up to the version of branching bisimilarity that does not require the preservation of divergence.

Investigation of In vitro Mineral forming bacterial isolates from supragingival calculus.

Science.gov (United States)

Baris, O; Demir, T; Gulluce, M

2017-12-01

Although it is known that bacterial mechanisms are involved in dental calculus formation, which is a predisposing factor in periodontal diseases, there have been few studies of such associations, and therefore, information available is limited. The purpose of this study was to isolate and identify aerobic bacteria responsible for direct calcification from supragingival calculus samples. The study was conducted using supragingival calculus samples from patients with periodontal disease, which was required as part of conventional treatment. Isolations were performed by sampling the supragingival calculus with buffer and inoculating the samples on media on which crystallization could be observed. The 16S recombinant DNA of the obtained pure cultures was then amplified and sequenced. A few bacterial species that have not previously been associated with mineralization or identified on bacterial plaque or calculus were detected. The bacteria that caused mineralization an aerobic environment are identified as Neisseria flava, Aggregatibacter segnis, Streptococcus tigurinus, and Morococcus cerebrosus. These findings proved that bacteria potentially play a role in the etiopathology of supragingival calculus. The association between the effects of the identified bacteria on periodontal diseases and calculus formation requires further studies.

Introduction to Integral Calculus Systematic Studies with Engineering Applications for Beginners

CERN Document Server

Rohde, Ulrich L; Poddar, Ajay K; Ghosh, A K

2011-01-01

An accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciences I ntegration is an important function of calculus, and Introduction to Integral Calculus combines fundamental concepts with scientific problems to develop intuition and skills for solving mathematical problems related to engineering and the physical sciences. The authors provide a solid introduction to integral calculus and feature applications of integration, solutions of differential equations, and evaluation methods. With logical organization coupled with cle

The proton structure function F sub 2 sup p (x, Q sup 2) at small x in the framework of extended Regge-Eikonal approach

CERN Document Server

Petrov, V A

2001-01-01

The behaviour of the proton structure function F sub 2 sup p (x, Q sup 2) in the region of small x is described in the framework of the generalized off-shell extention of the Regge-eikonal approach which automatically takes into account off-shell unitarity. A good quality is achieved of description of the experimental data for x < 10 sup - sup 2 and it is argued that the data on F sub 2 sup p (x, Q sup 2) measured at HERA can be fairly well described with classical universal Regge trajectories. No extra, hard trajectories of high intercept are needed for that. The x, Q sup 2 slopes and the effective intercept are discussed as functions of x and Q sup 2

Enabling quaternion derivatives: the generalized HR calculus

Science.gov (United States)

Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C.; Mandic, Danilo P.

2015-01-01

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis. PMID:26361555

Utilizing Microsoft Mathematics in Teaching and Learning Calculus

Science.gov (United States)

Oktaviyanthi, Rina; Supriani, Yani

2015-01-01

The experimental design was conducted to investigate the use of Microsoft Mathematics, free software made by Microsoft Corporation, in teaching and learning Calculus. This paper reports results from experimental study details on implementation of Microsoft Mathematics in Calculus, students' achievement and the effects of the use of Microsoft…

The development and nature of problem-solving among first-semester calculus students

Science.gov (United States)

Dawkins, Paul Christian; Mendoza Epperson, James A.

2014-08-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem

Advances in fractional calculus theoretical developments and applications in physics and engineering

CERN Document Server

Sabatier, J; Machado, J A Teneiro

2007-01-01

Fractional Calculus is a new growing field. Up to this point, researchers, scientists, and engineers have been reluctant to accept the fact that Fractional Calculus can be used in the analysis and design of many systems of practical interests, whereas in similar applications the traditional calculus either fails or provides poor solutionsMany engineers, scientists, and applied mathematicians are looking for books that can provide many applications of Fractional Calculus. This book will provide a partial solution to this problem. Since it covers recent applications of Fractional Calculus, it will be attractive to many engineers, scientists, and applied mathematicians.

Multivariate calculus and geometry

CERN Document Server

Dineen, Seán

2014-01-01

Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.

Representing and reasoning about program in situation calculus

Science.gov (United States)

Yang, Bo; Zhang, Ming-yi; Wu, Mao-nian; Xie, Gang

2011-12-01

Situation calculus is an expressive tool for modeling dynamical system in artificial intelligence, changes in a dynamical world is represented naturally by the notions of action, situation and fluent in situation calculus. Program can be viewed as a discrete dynamical system, so it is possible to model program with situation calculus. To model program written in a smaller core programming language CL, notion of fluent is expanded for representing value of expression. Together with some functions returning concerned objects from expressions, a basic action theory of CL programming is constructed. Under such a theory, some properties of program, such as correctness and termination can be reasoned about.

Reggeon calculus at collider energies

International Nuclear Information System (INIS)

Pajares, C.; Varias, A.; Yepes, P.

1983-01-01

The phenomenology of the perturbative reggeon calculus at collider energies is studied. It is found that the graphs which were neglected at ISR energies are still negligeable at √s=540 GeV. The perturbative series for the total cross section still converges reasonably fast. The values of the different parameters which describe rightly the data up to ISR energies give rise to a total cross section of around 60 mb at √s=540 GeV. For these values, the corresponding low mass and high mass eikonal series converges much more slowly. The non perturbative reggeon calculus gives rise to a total cross section less than 60 mb. (orig.)

Sequent Calculus and Equational Programming

Directory of Open Access Journals (Sweden)

Nicolas Guenot

2015-07-01

Full Text Available Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.

Golden quantum oscillator and Binet–Fibonacci calculus

International Nuclear Information System (INIS)

Pashaev, Oktay K; Nalci, Sengul

2012-01-01

The Binet formula for Fibonacci numbers is treated as a q-number and a q-operator with Golden ratio bases q = φ and Q = −1/φ, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given only by Fibonacci numbers. The ratio of successive energy levels is found to be the Golden sequence, and for asymptotic states in the limit n → ∞ it appears as the Golden ratio. We call this oscillator the Golden oscillator. Using double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived. Relations of Fibonacci calculus with a q-deformed fermion oscillator and entangled N-qubit states are indicated. (paper)

Golden quantum oscillator and Binet-Fibonacci calculus

Energy Technology Data Exchange (ETDEWEB)

Pashaev, Oktay K; Nalci, Sengul, E-mail: oktaypashaev@iyte.edu.tr [Department of Mathematics, Izmir Institute of Technology, Urla-Izmir 35430 (Turkey)

2012-01-13

The Binet formula for Fibonacci numbers is treated as a q-number and a q-operator with Golden ratio bases q = {phi} and Q = -1/{phi}, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given only by Fibonacci numbers. The ratio of successive energy levels is found to be the Golden sequence, and for asymptotic states in the limit n {yields} {infinity} it appears as the Golden ratio. We call this oscillator the Golden oscillator. Using double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived. Relations of Fibonacci calculus with a q-deformed fermion oscillator and entangled N-qubit states are indicated. (paper)

Advanced Placement Mathematics Calculus, Grade 12 Curriculum Guide.

Science.gov (United States)

Scharf, John; And Others

This document is a guide to the advanced placement program in calculus for grade 12 in the city schools in Warren, Ohio. The program covers analytic geometry, differential and integral calculus of algebraic functions, elementary transcendental functions, and applications of differentiation and integration. The philosophy and aims of the program…

DIFFERENTIAL AND INTEGRAL CALCULUS. A TENTATIVE CURRICULUM GUIDE.

Science.gov (United States)

BRANT, VINCENT; GERARDI, WILLIAM

A GUIDE FOR A 1-YEAR COURSE IN DIFFERENTIAL AND INTEGRAL CALCULUS PREREQUISITED KNOWLEDGE IN ALGEBRA, ANALYTIC TRIGONOMETRY, AND ELEMENTARY ANALYSIS. EACH ASSIGNMENT CONTAINED BOTH NEW AND REVIEW WORK TO REINFORCE THE NEW WORK. THERE WERE ELEVEN UNITS OF STUDY USING THE FOLLOWING FOUR BOOKS--"CALCULUS AND ANALYTIC GEOMETRY, THIRD…

Catwalk: First-Semester Calculus.

Science.gov (United States)

Speiser, Bob; Walter, Chuck

1994-01-01

Describes the use of time-lapse photographs of a running cat as a model to investigate the concepts of function and derivative in a college calculus course. Discusses student difficulties and implications for teachers. (MKR)

A study of ∇-discrete fractional calculus operator on the radial ...

African Journals Online (AJOL)

The fractional calculus includes concepts of integrals and derivatives of any complex or real order. The fractional calculus is as old as the usual calculus. Recently, many scientists have been studying on this eld to provide the development and applicability to various areas of mathematics, physics, engineering and other ...

Masses and Regge trajectories of triply heavy Ω{sub ccc} and Ω{sub bbb} baryons

Energy Technology Data Exchange (ETDEWEB)

Shah, Zalak; Rai, Ajay Kumar [Sardar Vallabhbhai National Institute of Technology, Department of Applied Physics, Surat, Gujarat (India)

2017-10-15

The excited state masses of triply charm and triply bottom Ω baryons are exhibited in the present study. The masses are computed for 1S-5S, 1P-5P, 1D-4D and 1F-2F states in the Hypercentral Constituent Quark Model (hCQM) with the hyper Coulomb plus linear potential. The triply charm/bottom baryon masses are experimentally unknown so that the Regge trajectories are plotted using computed masses to assign the quantum numbers of these unknown states. (orig.)

On certain fractional calculus operators involving generalized Mittag-Leffler function

OpenAIRE

Dinesh Kumar

2016-01-01

The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators are the generalization of the Saigo fractional calculus operators. The established results provide ex...

Coordinating Multiple Representations in a Reform Calculus Textbook

Science.gov (United States)

Chang, Briana L.; Cromley, Jennifer G.; Tran, Nhi

2016-01-01

Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions…

A phenomenological calculus of Wiener description space.

Science.gov (United States)

Richardson, I W; Louie, A H

2007-10-01

The phenomenological calculus is a categorical example of Robert Rosen's modeling relation. This paper is an alligation of the phenomenological calculus and generalized harmonic analysis, another categorical example. Our epistemological exploration continues into the realm of Wiener description space, in which constitutive parameters are extended from vectors to vector-valued functions of a real variable. Inherent in the phenomenology are fundamental representations of time and nearness to equilibrium.

Fractional and multivariable calculus model building and optimization problems

CERN Document Server

Mathai, A M

2017-01-01

This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable ...

Site specific mineral composition and microstructure of human supra-gingival dental calculus.

Science.gov (United States)

Hayashizaki, Junko; Ban, Seiji; Nakagaki, Haruo; Okumura, Akihiko; Yoshii, Saori; Robinson, Colin

2008-02-01

Dental calculus has been implicated in the aetiology of several periodontal conditions. Its prevention and removal are therefore desirable clinical goals. While it is known that calculus is very variable in chemical composition, crystallinity and crystallite size little is known about site specific variability within a dentition and between individuals. With this in mind, a study was undertaken to investigate the comparative site specific nature and composition of human dental supra-gingival dental calculus obtained from 66 male patients visiting for their dental check-up using fluorescent X-ray spectroscopy, X-ray diffractometry and Fourier transform infrared spectroscopy. The supra-gingival dental calculus formed on the lingual surfaces of lower anterior teeth and the buccal surfaces of upper molar teeth were classified into four types based on calcium phosphate phases present. There was significant difference in composition of the crystal phase types between lower and upper teeth (pdental calculus on anterior or molar teeth of all samples. The degree of crystallinity of dental calculus formed on the upper molar teeth was higher than that formed on the lower anterior teeth (pdental calculus formed on the lower anterior teeth were higher than on upper molar teeth (pdental supra-gingival dental calculus is related to its location in the mouth.

A many-sorted calculus based on resolution and paramodulation

CERN Document Server

Walther, Christoph

1987-01-01

A Many-Sorted Calculus Based on Resolution and Paramodulation emphasizes the utilization of advantages and concepts of many-sorted logic for resolution and paramodulation based automated theorem proving.This book considers some first-order calculus that defines how theorems from given hypotheses by pure syntactic reasoning are obtained, shifting all the semantic and implicit argumentation to the syntactic and explicit level of formal first-order reasoning. This text discusses the efficiency of many-sorted reasoning, formal preliminaries for the RP- and ?RP-calculus, and many-sorted term rewrit

Dental hygiene faculty calibration in the evaluation of calculus detection.

Science.gov (United States)

Garland, Kandis V; Newell, Kathleen J

2009-03-01

The purpose of this pilot study was to explore the impact of faculty calibration training on intra- and interrater reliability regarding calculus detection. After IRB approval, twelve dental hygiene faculty members were recruited from a pool of twenty-two for voluntary participation and randomized into two groups. All subjects provided two pre- and two posttest scorings of calculus deposits on each of three typodonts by recording yes or no indicating if they detected calculus. Accuracy and consistency of calculus detection were evaluated using an answer key. The experimental group received three two-hour training sessions to practice a prescribed exploring sequence and technique for calculus detection. Participants immediately corrected their answers, received feedback from the trainer, and reconciled missed areas. Intra- and interrater reliability (pre- and posttest) was determined using Cohen's Kappa and compared between groups using repeated measures (split-plot) ANOVA. The groups did not differ from pre- to posttraining (intrarater reliability p=0.64; interrater reliability p=0.20). Training had no effect on reliability levels for simulated calculus detection in this study. Recommendations for future studies of faculty calibration when evaluating students include using patients for assessing rater reliability, employing larger samples at multiple sites, and assessing the impact on students' attitudes and learning outcomes.

Calculus and Geometry

Indian Academy of Sciences (India)

IAS Admin

Sphere–Cylinder Theorem, vol- ume and surface area of the torus, volume and surface area of a slice of a solid sphere. The author earned his PhD degree in mathematics. (topology), in 2000, from. Panjab University,. Chandigarh and since then he has been teaching analysis, algebra, calculus and discrete mathematics at.

Effect of Ramadan fasting on urinary risk factors for calculus formation.

Science.gov (United States)

Miladipour, Amir Hossein; Shakhssalim, Nasser; Parvin, Mahmoud; Azadvari, Mohaddeseh

2012-01-01

Even though dehydration could aggravate formation of urinary calculi, the effects of fluid and food restriction on calculus formation is not thoroughly defined. The purpose of this study is to evaluate the effects of fluid and food restriction in Ramadan fasting on urinary factors in kidney and urinary calculus formation. Fifty-seven men aged 30 to 55 years old, including 37 recurrent calcium calculus formers and 20 with no history of kidney calculi were evaluated for blood tests, ultrasonography investigations, urinalysis, urine culture, and also 24-hour urine collection test. Metabolites including calcium, oxalate, citrate, uric acid, magnesium, phosphate, potassium, sodium, and creatinine were measured before and during Ramadan fasting. The values of calculus-precipitating solutes as well as inhibitory factors were documented thoroughly. Total excretion of calcium, phosphate, and magnesium in 24-hour urine and also urine volume during fasting were significantly lower than those in the nonfasting period. Urine concentration of calcium during fasting was significantly lower than nonfasting (P calculus formation. We did not find enough evidence in favor of increased risks of calculus formation during Ramadan fasting.

Probabilistic Analysis of the Quality Calculus

DEFF Research Database (Denmark)

Nielson, Hanne Riis; Nielson, Flemming

2013-01-01

We consider a fragment of the Quality Calculus, previously introduced for defensive programming of software components such that it becomes natural to plan for default behaviour in case the ideal behaviour fails due to unreliable communication. This paper develops a probabilistically based trust...... analysis supporting the Quality Calculus. It uses information about the probabilities that expected input will be absent in order to determine the trustworthiness of the data used for controlling the distributed system; the main challenge is to take accord of the stochastic dependency between some...

Multivariable dynamic calculus on time scales

CERN Document Server

Bohner, Martin

2016-01-01

This book offers the reader an overview of recent developments of multivariable dynamic calculus on time scales, taking readers beyond the traditional calculus texts. Covering topics from parameter-dependent integrals to partial differentiation on time scales, the book’s nine pedagogically oriented chapters provide a pathway to this active area of research that will appeal to students and researchers in mathematics and the physical sciences. The authors present a clear and well-organized treatment of the concept behind the mathematics and solution techniques, including many practical examples and exercises.

Fisher information, Borges operators, and q-calculus

Science.gov (United States)

Pennini, F.; Plastino, A.; Ferri, G. L.

2008-10-01

We discuss applying the increasingly popular q-calculus, or deformed calculus, so as to suitably generalize Fisher’s information measure and the Cramer-Rao inequality. A q-deformation can be attained in multiple ways, and we show that most of them do not constitute legitimate procedures. Within such a context, the only completely acceptable q-deformation is that ensuing from using the so-called Borges derivative [E.P. Borges, Physica A 340 (2004) 95].

Reggeon calculus as a low-order perturbation theory for the Pomeron

International Nuclear Information System (INIS)

DeTar, C.

1975-01-01

We review the foundations of the Gribov Reggeon calculus with an emphasis on the relationship between the energy-plane and J-plane descriptions of the diagrams of the calculus. The question of the ''large-rapidity-gap cutoff'' for the Pomeron and the problem of signature are treated in more detail than in the traditional approach to the calculus. Except for some slight differences, the main results agree with Gribov's original formulation. We advocate the use of the Reggeon calculus as a refinement on the contemporary ''two-component'' model for the Pomeron and collect some formulas useful for phenomenological applications

Secure Data Flow in a Calculus for Context Awareness

DEFF Research Database (Denmark)

Bucur, Doina; Nielsen, Mogens

2008-01-01

We present a Mobile-Ambients-based process calculus to describe context-aware computing in an infrastructure-based Ubiquitous Computing setting. In our calculus, computing agents can provide and discover contextual information and are owners of security policies. Simple access control to contextual...

Visual Thinking and Gender Differences in High School Calculus

Science.gov (United States)

Haciomeroglu, Erhan Selcuk; Chicken, Eric

2012-01-01

This study sought to examine calculus students' mathematical performances and preferences for visual or analytic thinking regarding derivative and antiderivative tasks presented graphically. It extends previous studies by investigating factors mediating calculus students' mathematical performances and their preferred modes of thinking. Data were…

Metric regularity and subdifferential calculus

International Nuclear Information System (INIS)

Ioffe, A D

2000-01-01

The theory of metric regularity is an extension of two classical results: the Lyusternik tangent space theorem and the Graves surjection theorem. Developments in non-smooth analysis in the 1980s and 1990s paved the way for a number of far-reaching extensions of these results. It was also well understood that the phenomena behind the results are of metric origin, not connected with any linear structure. At the same time it became clear that some basic hypotheses of the subdifferential calculus are closely connected with the metric regularity of certain set-valued maps. The survey is devoted to the metric theory of metric regularity and its connection with subdifferential calculus in Banach spaces

The dental calculus metabolome in modern and historic samples.

Science.gov (United States)

Velsko, Irina M; Overmyer, Katherine A; Speller, Camilla; Klaus, Lauren; Collins, Matthew J; Loe, Louise; Frantz, Laurent A F; Sankaranarayanan, Krithivasan; Lewis, Cecil M; Martinez, Juan Bautista Rodriguez; Chaves, Eros; Coon, Joshua J; Larson, Greger; Warinner, Christina

2017-01-01

Dental calculus is a mineralized microbial dental plaque biofilm that forms throughout life by precipitation of salivary calcium salts. Successive cycles of dental plaque growth and calcification make it an unusually well-preserved, long-term record of host-microbial interaction in the archaeological record. Recent studies have confirmed the survival of authentic ancient DNA and proteins within historic and prehistoric dental calculus, making it a promising substrate for investigating oral microbiome evolution via direct measurement and comparison of modern and ancient specimens. We present the first comprehensive characterization of the human dental calculus metabolome using a multi-platform approach. Ultra performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS) quantified 285 metabolites in modern and historic (200 years old) dental calculus, including metabolites of drug and dietary origin. A subset of historic samples was additionally analyzed by high-resolution gas chromatography-MS (GC-MS) and UPLC-MS/MS for further characterization of metabolites and lipids. Metabolite profiles of modern and historic calculus were compared to identify patterns of persistence and loss. Dipeptides, free amino acids, free nucleotides, and carbohydrates substantially decrease in abundance and ubiquity in archaeological samples, with some exceptions. Lipids generally persist, and saturated and mono-unsaturated medium and long chain fatty acids appear to be well-preserved, while metabolic derivatives related to oxidation and chemical degradation are found at higher levels in archaeological dental calculus than fresh samples. The results of this study indicate that certain metabolite classes have higher potential for recovery over long time scales and may serve as appropriate targets for oral microbiome evolutionary studies.

Solitary main pancreatic ductal calculus of possible biliary origin causing acute pancreatitis.

Science.gov (United States)

Chaparala, Ramakrishna Prasad Chowdary; Patel, Rafiuddin; Guthrie, James Ahsley; Davies, Mervyn Huw; Guillou, Pierre J; Menon, Krishna V

2005-09-10

Pancreatic ductal calculi are most often associated with chronic pancreatitis. Radiological features of chronic pancreatitis are readily evident in the presence of these calculi. However, acute pancreatitis due to a solitary main pancreatic ductal calculus of biliary origin is rare. A 59-year-old man presented with a first episode of acute pancreatitis. Contrast enhanced computerized tomography (CT) scan and endoscopic retrograde cholangiopancreatography (ERCP) revealed a calculus in the main pancreatic duct in the head of the pancreas causing acute pancreatitis. There were no features suggestive of chronic pancreatitis on CT scanning. The episode acute pancreatitis was managed conservatively. ERCP extraction of the calculus failed as the stone was impacted in the main pancreatic duct resulting in severe acute pancreatitis. Once this resolved, a transduodenal exploration and extraction of the pancreatic ductal calculus was performed successfully. Crystallographic analysis revealed the composition of the calculus was different to that seen in chronic pancreatitis, but more in keeping with a calculus of biliary origin. This could be explained by migration of the biliary calculus via the common channel into the main pancreatic duct. Following the operation the patient made an uneventful recovery and was well at two-year follow up. Acute pancreatitis due to a solitary main pancreatic ductal calculus of biliary origin is rare. Failing endoscopic extraction, transduodenal exploration and extraction is a safe option after resolution of acute pancreatitis.

Calculus

CERN Document Server

Zandy, Bernard V

2003-01-01

We take great notes-and make learning a snap When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core Calculus concepts-from functions, limits, and derivatives to differentials, integration, and definite integrals- and get the best possible grade. At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented writers who know how to cut to the chase- and zero in on the essential information you need to succeed.

Duality and calculus of convex objects (theory and applications)

International Nuclear Information System (INIS)

Brinkhuis, Ya; Tikhomirov, V M

2007-01-01

A new approach to convex calculus is presented, which allows one to treat from a single point of view duality and calculus for various convex objects. This approach is based on the possibility of associating with each convex object (a convex set or a convex function) a certain convex cone without loss of information about the object. From the duality theorem for cones duality theorems for other convex objects are deduced as consequences. The theme 'Duality formulae and the calculus of convex objects' is exhausted (from a certain precisely formulated point of view). Bibliography: 5 titles.

Giant vesical calculus

African Journals Online (AJOL)

Giant vesical calculus. A case report. H. H. LAUBSCHER. Summary. An exceptional case of bladder stone is presented. The case is unusual as regards the size of the stone and the fact that the patient did··not seek medical assistance much earlier, as this was readily avail- able. Furthermore, recovery after removal of the.

Preservation of the metaproteome: variability of protein preservation in ancient dental calculus.

Science.gov (United States)

Mackie, Meaghan; Hendy, Jessica; Lowe, Abigail D; Sperduti, Alessandra; Holst, Malin; Collins, Matthew J; Speller, Camilla F

2017-01-01

Proteomic analysis of dental calculus is emerging as a powerful tool for disease and dietary characterisation of archaeological populations. To better understand the variability in protein results from dental calculus, we analysed 21 samples from three Roman-period populations to compare: 1) the quantity of extracted protein; 2) the number of mass spectral queries; and 3) the number of peptide spectral matches and protein identifications. We found little correlation between the quantity of calculus analysed and total protein identifications, as well as no systematic trends between site location and protein preservation. We identified a wide range of individual variability, which may be associated with the mechanisms of calculus formation and/or post-depositional contamination, in addition to taphonomic factors. Our results suggest dental calculus is indeed a stable, long-term reservoir of proteins as previously reported, but further systematic studies are needed to identify mechanisms associated with protein entrapment and survival in dental calculus.

Effect of non-functional teeth on accumulation of supra-gingival calculus in children.

Science.gov (United States)

Ashkenazi, M; Miller, R; Levin, L

2012-10-01

To evaluate the occurrence of supra-gingival calculus in children aged 6-9 years with disuse conditions such as: presence of dental pain, open-bite or erupting teeth. A cohort of 327 children aged 7.64±2.12 (range: 6-9) years (45% girls) were screened for presence of supra-gingival calculus in relation to open bite, erupting teeth and dental pain. Presence of dental calculus was evaluated dichotomically in the buccal, palatinal/lingual and occlusal surfaces. Plaque index (PI) and gingival index (GI) were also evaluated. Supra-gingival calculus was found in 15.9% of the children mainly in the mandibular incisors. Children aged 6-7 years had a higher prevalence of calculus as compared to children aged 7-8 years (23% vs. 13.5%, p=0.057) or 8-9 years (23% vs. 12.4%, p=0.078), respectively. No statistical relation was found between plaque and gingival indices and presence of calculus. The prevalence of calculus among children with openbite was significantly higher than that of children without open-bite (29.4% vs. 10.7%, p=0.0006, OR=3.489). The prevalence of calculus among children with erupting teeth in their oral cavity was higher than that of children without erupting teeth (17.7% vs. 9%, respectively, p=0.119). No statistical correlation was found between presence of dental pain and calculus (15.4% vs. 15.9%; p=0.738). Accumulation of calculus in children aged 6-10 years was found mainly in the mandibular incisors, decreased with age and was correlated with open-bite.

[Percentage of uric acid calculus and its metabolic character in Dongjiang River valley].

Science.gov (United States)

Chong, Hong-Heng; An, Geng

2009-02-15

To study the percentage of uric acid calculus in uroliths and its metabolic character in Dongjiang River valley. To analyze the chemical composition of 290 urinary stones by infrared (IR) spectroscopy and study the ratio changes of uric acid calculus. Uric acid calculus patients and healthy people were studied. Personal characteristics, dietary habits were collected. Conditional logistic regression was used for data analysis and studied the dietary risk factors of uric acid calculus. Patients with uric acid calculus, calcium oxalate and those without urinary calculus were undergone metabolic evaluation analysis. The results of uric acid calculus patients compared to another two groups to analysis the relations between the formation of uric acid calculus and metabolism factors. Uric acid calculi were found in 53 cases (18.3%). The multiple logistic regression analysis suggested that low daily water intake, eating more salted and animal food, less vegetable were very closely associated with uric acid calculus. Comparing to calcium oxalate patients, the urine volume, the value of pH, urine calcium, urine oxalic acid were lower, but uric acid was higher than it. The value of pH, urine oxalic acid and citric acid were lower than them, but uric acid and urine calcium were higher than none urinary calculus peoples. Blood potassium and magnesium were lower than them. The percentage of uric acid stones had obvious advanced. Less daily water intake, eating salted food, eating more animal food, less vegetables and daily orange juice intake, eating sea food are the mainly dietary risk factors to the formation of uric acid calculus. Urine volume, the value of pH, citric acid, urine calcium, urine uric acid and the blood natrium, potassium, magnesium, calcium, uric acid have significant influence to the information of uric acid stones.

Fuzzy relational calculus theory, applications and software

CERN Document Server

Peeva, Ketty

2004-01-01

This book examines fuzzy relational calculus theory with applications in various engineering subjects. The scope of the text covers unified and exact methods with algorithms for direct and inverse problem resolution in fuzzy relational calculus. Extensive engineering applications of fuzzy relation compositions and fuzzy linear systems (linear, relational and intuitionistic) are discussed. Some examples of such applications include solutions of equivalence, reduction and minimization problems in fuzzy machines, pattern recognition in fuzzy languages, optimization and inference engines in textile and chemical engineering, etc. A comprehensive overview of the authors' original work in fuzzy relational calculus is also provided in each chapter. The attached CD-Rom contains a toolbox with many functions for fuzzy calculations, together with an original algorithm for inverse problem resolution in MATLAB. This book is also suitable for use as a textbook in related courses at advanced undergraduate and graduate level...

Selective ablation of dental calculus with a frequency-doubled Alexandrite laser

Science.gov (United States)

Rechmann, Peter; Hennig, Thomas

1996-01-01

The aim of the study was the selective removal of dental calculus by means of pulsed lasers. In a first approach the optical characteristics of subgingival calculus were calculated using fluorescence emission spectroscopy (excitation laser: N2-laser, wavelength 337 nm, pulse duration 4 ns). Subgingival calculus seems to absorb highly in the ultraviolet spectral region up to 420 nm. According to these measurements a frequency doubled Alexandrite-laser (wavelength 377 nm, pulse duration 100 ns, repetition rate 110 Hz) was used to irradiate calculus located on enamel, at the cementum enamel junction and on the root surface (located on dentin or on cementum). Irradiation was performed perpendicular to the root surface with a laser fluence of 1 Jcm-2. During the irradiation procedure an effective water cooling-system was engaged. Histological investigations were done on undecalcified sections. As a result, engaging low fluences allows a fast and strictly selective removal of subgingival calculus. Even more the investigations revealed that supragingival calculus can be removed in a strictly selective manner engaging a frequency doubled Alexandrite-laser. No adverse side effects to the surrounding tissues could be found.

Prostatic fossa calculus | El Abiad | Pan African Medical Journal

African Journals Online (AJOL)

As part of the evaluation, a plain radiograph was performed and incidentally showed a radiopaque prostatic calculus (Red arrows). A retrograde urethrocystography, performed after a 10-days course of antibiotics, confirmed the presence of an approximately 35 mm non-obstructive calculus occupying almost the whole ...

A compositional proof system for the modal μ-calculus

DEFF Research Database (Denmark)

Andersen, Henrik Reif; Stirling, C.; Winskel,, G.

1994-01-01

We present a proof system for determining satisfaction between processes in a fairly general process algebra and assertions of the modal μ-calculus. The proof system is compositional in the structure of processes. It extends earlier work on compositional reasoning within the modal μ-calculus and ...

Non-commutative residue of projections in Boutet de Monvel's calculus

DEFF Research Database (Denmark)

Gaarde, Anders

2007-01-01

Using results by Melo, Nest, Schick, and Schrohe on the K-theory of Boutet de Monvel's calculus of boundary value problems, we show that the non-commutative residue introduced by Fedosov, Golse, Leichtnam, and Schrohe vanishes on projections in the calculus. This partially answers a question raised...... in a recent collaboration with Grubb, namely whether the residue is zero on sectorial projections for boundary value problems: This is confirmed to be true when the sectorial projections is in the calculus....

Application of Quantum Process Calculus to Higher Dimensional Quantum Protocols

Directory of Open Access Journals (Sweden)

Simon J. Gay

2014-07-01

Full Text Available We describe the use of quantum process calculus to describe and analyze quantum communication protocols, following the successful field of formal methods from classical computer science. We have extended the quantum process calculus to describe d-dimensional quantum systems, which has not been done before. We summarise the necessary theory in the generalisation of quantum gates and Bell states and use the theory to apply the quantum process calculus CQP to quantum protocols, namely qudit teleportation and superdense coding.

Stochastic integration by parts and functional Itô calculus

CERN Document Server

Vives, Josep

2016-01-01

This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2012). The notes of the course by Vlad Bally, co-authored with Lucia Caramellino, develop integration by parts formulas in an abstract setting, extending Malliavin's work on abstract Wiener spaces. The results are applied to prove absolute continuity and regularity results of the density for a broad class of random processes. Rama Cont's notes provide an introduction to the Functional Itô Calculus, a non-anticipative functional calculus that extends the classical Itô calculus to path-dependent functionals of stochastic processes. This calculus leads to a new class of path-dependent partial differential equations, termed Functional Kolmogorov Equations, which arise in the study of martingales and forward-backward stochastic differential equations. This book will appeal to both young and senior researchers in probability and stochastic processes, as well as to pract...

Quantum calculus new concepts, impulsive IVPs and BVPs, inequalities

CERN Document Server

Ahmad, Bashir; Tariboon, Jessada

2016-01-01

The main objective of this book is to extend the scope of the q-calculus based on the definition of q-derivative [Jackson (1910)] to make it applicable to dense domains. As a matter of fact, Jackson's definition of q-derivative fails to work for impulse points while this situation does not arise for impulsive equations on q-time scales as the domains consist of isolated points covering the case of consecutive points. In precise terms, we study quantum calculus on finite intervals.In the first part, we discuss the concepts of qk-derivative and qk-integral, and establish their basic properties. As applications, we study initial and boundary value problems of impulsive qk-difference equations and inclusions equipped with different kinds of boundary conditions. We also transform some classical integral inequalities and develop some new integral inequalities for convex functions in the context of qk-calculus. In the second part, we develop fractional quantum calculus in relation to a new qk-shifting operator and e...

Metaphor Clusters: Characterizing Instructor Metaphorical Reasoning on Limit Concepts in College Calculus

Science.gov (United States)

Patel, Rita Manubhai; McCombs, Paul; Zollman, Alan

2014-01-01

Novice students have difficulty with the topic of limits in calculus. We believe this is in part because of the multiple perspectives and shifting metaphors available to solve items correctly. We investigated college calculus instructors' personal concepts of limits. Based upon previous research investigating introductory calculus student…

The Development and Nature of Problem-Solving among First-Semester Calculus Students

Science.gov (United States)

Dawkins, Paul Christian; Epperson, James A. Mendoza

2014-01-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate…

On asymptotic solutions of Regge field theory in zero transverse dimensions

International Nuclear Information System (INIS)

Bondarenko, S.; Horwitz, L.; Levitan, J.; Yahalom, A.

2013-01-01

An investigation of dynamical properties of solutions of a toy model of interacting Pomerons with triple vertex in zero transverse dimension is performed. Stable points and corresponding solutions at the limit of large rapidity are studied in the framework of a given model. It is shown that, at large rapidity, the “fan” amplitude is also a leading solution for the full RFT-0 (Regge Field Theory in zero transverse dimensions) Hamiltonian with both vertices of Pomeron splitting and merging included. An analytical form of the symmetrical solution of the equations of motion at high energy is obtained as well. For the solutions we have found, the scattering amplitude at large values of rapidity is calculated. Stability of the solutions is investigated by Lyapunov functions and the presence of closed cycles in solutions is demonstrated by the new method

Regge meets collinear in strongly-coupled N=4 super Yang-Mills

Energy Technology Data Exchange (ETDEWEB)

Sprenger, Martin [Institut für Theoretische Physik, Eidgenössische Technische Hochschule Zürich,Wolfgang-Pauli-Strasse 27, 8093 Zürich (Switzerland)

2017-01-10

We revisit the calculation of the six-gluon remainder function in planar N=4 super Yang-Mills theory from the strong coupling TBA in the multi-Regge limit and identify an infinite set of kinematically subleading terms. These new terms can be compared to the strong coupling limit of the finite-coupling expressions for the impact factor and the BFKL eigenvalue proposed by Basso et al. in https://www.doi.org/10.1007/JHEP01(2015)027, which were obtained from an analytic continuation of the Wilson loop OPE. After comparing the results order by order in those subleading terms, we show that it is possible to precisely map both formalisms onto each other. A similar calculation can be carried out for the seven-gluon amplitude, the result of which shows that the central emission vertex does not become trivial at strong coupling.

Diphoton production at Tevatron in the quasi-multiple-Regge-kinematics approach

Energy Technology Data Exchange (ETDEWEB)

Saleev, V.A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Samarskij Gosudarstvennyj Univ., Samara (Russian Federation)

2009-12-15

We study the production of prompt diphotons in the central region of rapidity within the frame- work of the quasi-multi-Regge-kinematics approach applying the hypothesis of quark and gluon Reggeization. We describe accurately and without free parameters the experimental data which were obtained by the CDF Collaboration at the Tevatron Collider. It is shown that the main contribution to studied process is given by the direct fusion of two Reggeized gluons into a photon pair, which is described by the effective Reggeon-Reggeon to particle-particle vertex. The contribution from the annihilation of Reggeized quark-antiquark pair into a diphoton is also considered. At the stage of numerical calculations we use the Kimber-Martin-Ryskin prescription for unintegrated quark and gluon distribution functions, with the Martin-Roberts-Stirling-Thorne collinear parton densities for a proton as input. (orig.)

Dynamical equations for a Regge theory with crossing symmetry and unitarity. II. The case of strong coupling, and elimination of ghost poles

International Nuclear Information System (INIS)

Johnson, P.W.; Warnock, R.L.

1977-01-01

Equations for the construction of a crossing-symmetric unitary Regge theory of meson-meson scattering are described. In the case of strong coupling, Regge trajectories are to be generated dynamically as zeros of the D function in a nonlinear N/D system. This paper is concerned mainly with writing the inputs to the N/D system in such a way that a convergent theory with exact crossing symmetry is defined. The scheme demands elimination of ghosts, i.e., bound-state poles at energies below threshold where trajectories pass through zero. A method for ghost elimination is proposed which entails an s-wave subtraction constant, and allows the physical s wave to be different from the l-analytic amplitude evaluated at l = 0. A dynamical model is suggested in which the subtraction constant alone generates the meson-meson interaction. An alternative ghost-elimination scheme proposed by Gell-Mann, in which only l-analytic amplitudes are involved, can be discussed in a formalism including channels with spin

Tracing back resonances to families of Regge trajectories. New finite energy sum rules

International Nuclear Information System (INIS)

Mandelbrojt, Jacques.

1975-04-01

An amplitude is supposed to be expressed for large enough energies as a sum of contributions of Regge poles. Calling family of trajectories the set of trajectories which differ by integers from one of them, a correspondance, such that the energy and width of a given resonance depend on only family of trajectories, is established between resonances of the amplitude and families of trajectories. The contribution to the amplitude of each family of trajectories is shown to satisfy the same finite energy sum rules as does the amplitude itself. In these sum rules the resonance approximation can be made where the only resonances that will appear are those which are in correspondence with the family [fr

Recalling Prerequisite Material in a Calculus II Course to Improve Student Success

Science.gov (United States)

Mokry, Jeanette

2016-01-01

This article discusses preparation assignments used in a Calculus II course that cover material from prerequisite courses. Prior to learning new material, students work on problems outside of class involving concepts from algebra, trigonometry, and Calculus I. These problems are directly built upon in order to answer Calculus II questions,…

The Path to College Calculus: The Impact of High School Mathematics Coursework

Science.gov (United States)

Sadler, Philip; Sonnert, Gerhard

2018-01-01

This study addresses a longstanding question among high school mathematics teachers and college mathematics professors: Which is the best preparation for college calculus-- (a) a high level of mastery of mathematics considered preparatory for calculus (algebra, geometry, precalculus) or (b) taking calculus itself in high school? We used a data set…

A Generalized Nonlocal Calculus with Application to the Peridynamics Model for Solid Mechanics

OpenAIRE

Alali, Bacim; Liu, Kuo; Gunzburger, Max

2014-01-01

A nonlocal vector calculus was introduced in [2] that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A generalization is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal...

Type Inference for Session Types in the Pi-Calculus

DEFF Research Database (Denmark)

Graversen, Eva Fajstrup; Harbo, Jacob Buchreitz; Huttel, Hans

2014-01-01

In this paper we present a direct algorithm for session type inference for the π-calculus. Type inference for session types has previously been achieved by either imposing limitations and restriction on the π-calculus, or by reducing the type inference problem to that for linear types. Our approach...

ANALYTICAL MODEL FOR LATHE TOOL DISPLACEMENTS CALCULUS IN THE MANUFACTURING P ROCESS

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Catălin ROŞU

2014-01-01

Full Text Available In this paper, we present an analytical model for lathe tools displacements calculus in the manufacturing process. We will present step by step the methodology for the displacements calculus and in the end we will insert these relations in a program for automatic calculus and we extract the conclusions. There is taken into account only the effects of the bending moments (because these insert the highest displacements. The simplifying assumptions and the calculus relations for the displacements (linea r and angular ones are presented in an original way.

Complete staghorn calculus in polycystic kidney disease: infection is still the cause.

Science.gov (United States)

Mao, Zhiguo; Xu, Jing; Ye, Chaoyang; Chen, Dongping; Mei, Changlin

2013-08-01

Kidney stones in patients with autosomal dominant polycystic kidney disease are common, regarded as the consequence of the combination of anatomic abnormality and metabolic risk factors. However, complete staghorn calculus is rare in polycystic kidney disease and predicts a gloomy prognosis of kidney. For general population, recent data showed metabolic factors were the dominant causes for staghorn calculus, but for polycystic kidney disease patients, the cause for staghorn calculus remained elusive. We report a case of complete staghorm calculus in a polycystic kidney disease patient induced by repeatedly urinary tract infections. This 37-year-old autosomal dominant polycystic kidney disease female with positive family history was admitted in this hospital for repeatedly upper urinary tract infection for 3 years. CT scan revealed the existence of a complete staghorn calculus in her right kidney, while there was no kidney stone 3 years before, and the urinary stone component analysis showed the composition of calculus was magnesium ammonium phosphate. UTI is an important complication for polycystic kidney disease and will facilitate the formation of staghorn calculi. As staghorn calculi are associated with kidney fibrosis and high long-term renal deterioration rate, prompt control of urinary tract infection in polycystic kidney disease patient will be beneficial in preventing staghorn calculus formation.

Model checking biological systems described using ambient calculus

DEFF Research Database (Denmark)

Mardare, Radu Iulian; Priami, Corrado; Qualia, Paola

2005-01-01

Model checking biological systems described using ambient calculus. In Proc. of the second International Workshop on Computational Methods in Systems Biology (CMSB04), Lecture Notes in Bioinformatics 3082:85-103, Springer, 2005.......Model checking biological systems described using ambient calculus. In Proc. of the second International Workshop on Computational Methods in Systems Biology (CMSB04), Lecture Notes in Bioinformatics 3082:85-103, Springer, 2005....

Eye Irritation Test of Bovis Calculus Pharmacopuncture Solutions for Eye Drop

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Hyeong-sik Seo

2008-06-01

Full Text Available Objective : This study was done to investigate the safety of Bovis Calculus pharmacopuncture solution manufactured with freezing dryness method to use eye drop. Methods : The eye irritation test of this material was performed according to the Regulation of Korea Food & Drug Administration (2005. 10. 21, KFDA 2005-60. After Bovis Calculus pharmacopuncture solution was medicated in the left eye of the rabbits, the auther observed eye irritation of the cornea, iris, conjunctiva at 1, 2, 3, 4 & 7day. Results : 1. After Bovis Calculus pharmacopuncture solution was medicated in the left eye of the rabbits, there wasn’t physical problem at 9 rabbits. 2. After Bovis Calculus pharmacopuncture solutionwas medicated in the left eye of the rabbits, there wasn’t eye irritation of the cornea, iris, conjunctiva at 1, 2, 3, 4 & 7day. Conclusions : I suggested that Bovis Calculus pharmacopuncture solution didn’t induced eye irritation in rabbits.

Bacterial Viability within Dental Calculus: An Untrodden, Inquisitive Clinico-Patho- Microbiological Research.

Science.gov (United States)

Gupta, Swati; Jain, P K; Kumra, Madhumani; Rehani, Shweta; Mathias, Yulia; Gupta, Ramakant; Mehendiratta, Monica; Chander, Anil

2016-07-01

Chronic inflammatory periodontal diseases i.e. gingivitis and periodontitis are one of the most common afflictions faced by human beings. Dental plaque, which is a pool of pathogenic microorganisms, remains to be current mainstay in etiopathogenesis. Dental calculus, which is a mineralized product of this plaque remains ignored and is considered merely as an ash heap of minor significance. However, the intriguing array in disease etiopathogenesis bulldozed researchers to suspect the role of calculus in disease chrysalis but still the viability of bacteria inside calculus and thus its pathogenicity remains an intricacy; the answer to which lies in the Pandora's Box. The present study was undertaken to investigate the viability of bacteria within dental calculus along with their identification. Also, to classify dental calculus on the basis of mineralization and to observe the variation of viable microflora found in dental calculus with the extent of mineralization and disease severity. A total of 60 samples were obtained, by harvesting two samples of supragingival calculus from each patient having chronic inflammatory periodontal disease. These samples were divided into two groups (Group A and Group B). Samples of Group A were kept non-irradiated and samples of Group B were exposed to UV radiation. The samples were categorized into less, moderately and highly mineralized according to the force required for crushing them. All the crushed calculus samples were then divided into three parts. These were used for dark-field microscopy, gram staining and bacterial cultures. Bacterial identification of the cultures obtained was also carried out by performing various biochemical assays. The present study revealed the presence of motile spirochaetes within the samples under dark-field microscope. Gram staining revealed presence of numerous gram positive cocci and gram negative bacilli. Bacterial cultures showed growth of variety of aerobic and capnophilic microorganisms. The

Unfolding Semantics of the Untyped λ-Calculus with lectrec-Calculus with letrec

NARCIS (Netherlands)

Rochel, J.

2016-01-01

We investigate the relationship between finite terms in lambda-letrec, the lambda calculus with letrec, and the infinite lambda terms they express. We say that a lambda-letrec term expresses a lambda term if the latter can be obtained as an infinite unfolding of the former. Unfolding is the process

Means and Variances without Calculus

Science.gov (United States)

Kinney, John J.

2005-01-01

This article gives a method of finding discrete approximations to continuous probability density functions and shows examples of its use, allowing students without calculus access to the calculation of means and variances.

QPFT operator algebras and commutative exterior differential calculus

International Nuclear Information System (INIS)

Yur'ev, D.V.

1993-01-01

The reduction of the structure theory of the operator algebras of quantum projective (sl(2, C)-invariant) field theory (QPFT operator algebras) to a commutative exterior differential calculus by means of the operation of renormalization of a pointwise product of operator fields is described. In the first section, the author introduces the concept of the operator algebra of quantum field theory and describes the operation of the renormalization of a pointwise product of operator fields. The second section is devoted to a brief exposition of the fundamentals of the structure theory of QPT operator algebras. The third section is devoted to commutative exterior differential calculus. In the fourth section, the author establishes the connection between the renormalized pointwise product of operator fields in QPFT operator algebras and the commutative exterior differential calculus. 5 refs

Regularization of positive definite matrix fields based on multiplicative calculus

NARCIS (Netherlands)

Florack, L.M.J.; Bruckstein, A.M.; Haar Romeny, ter B.M.; Bronstein, A.M.; Bronstein, M.M.

2012-01-01

Multiplicative calculus provides a natural framework in problems involving positive images and positivity preserving operators. In increasingly important, complex imaging frameworks, such as diffusion tensor imaging, it complements standard calculus in a nontrivial way. The purpose of this article

Crystalline structure of pulverized dental calculus induces cell death in oral epithelial cells.

Science.gov (United States)

Ziauddin, S M; Yoshimura, A; Montenegro Raudales, J L; Ozaki, Y; Higuchi, K; Ukai, T; Kaneko, T; Miyazaki, T; Latz, E; Hara, Y

2018-06-01

Dental calculus is a mineralized deposit attached to the tooth surface. We have shown that cellular uptake of dental calculus triggers nucleotide-binding oligomerization domain-like receptor family pyrin domain-containing 3 (NLRP3) inflammasome activation, leading to the processing of the interleukin-1β precursor into its mature form in mouse and human phagocytes. The activation of the NLRP3 inflammasome also induced a lytic form of programmed cell death, pyroptosis, in these cells. However, the effects of dental calculus on other cell types in periodontal tissue have not been investigated. The aim of this study was to determine whether dental calculus can induce cell death in oral epithelial cells. HSC-2 human oral squamous carcinoma cells, HOMK107 human primary oral epithelial cells and immortalized mouse macrophages were exposed to dental calculus or 1 of its components, hydroxyapatite crystals. For inhibition assays, the cells were exposed to dental calculus in the presence or absence of cytochalasin D (endocytosis inhibitor), z-YVAD-fmk (caspase-1 inhibitor) or glyburide (NLRP3 inflammasome inhibitor). Cytotoxicity was determined by measuring lactate dehydrogenase (LDH) release and staining with propidium iodide. Tumor necrosis factor-α production was quantified by enzyme-linked immunosorbent assay. Oral epithelial barrier function was examined by permeability assay. Dental calculus induced cell death in HSC-2 cells, as judged by LDH release and propidium iodide staining. Dental calculus also induced LDH release from HOMK107 cells. Following heat treatment, dental calculus lost its capacity to induce tumor necrosis factor-α in mouse macrophages, but could induce LDH release in HSC-2 cells, indicating a major role of inorganic components in cell death. Hydroxyapatite crystals also induced cell death in both HSC-2 and HOMK107 cells, as judged by LDH release, indicating the capacity of crystal particles to induce cell death. Cell death induced by dental

A Calculus of Circular Proofs and its Categorical Semantics

DEFF Research Database (Denmark)

Santocanale, Luigi

2002-01-01

We present a calculus of "circular proofs": the graph underlying a proof is not a finite tree but instead it is allowed to contain a certain amount of cycles.The main challenge in developing a theory for the calculus is to define the semantics of proofs, since the usual method by induction...

A Calculus of Circular Proofs and its Categorical Semantics

DEFF Research Database (Denmark)

Santocanale, Luigi

2002-01-01

We present a calculus of “circular proofs”: the graph underlying a proof is not a finite tree but instead it is allowed to contain a certain amount of cycles.The main challenge in developing a theory for the calculus is to define the semantics of proofs, since the usual method by induction...

Descartes' Calculus of Subnormals: What Might Have Been

Science.gov (United States)

Boudreaux, Gregory Mark; Walls, Jess E.

2013-01-01

Rene Descartes' method for finding tangents (equivalently, subnormals) depends on geometric and algebraic properties of a family of circles intersecting a given curve. It can be generalized to establish a calculus of subnormals, an alternative to the calculus of Newton and Leibniz. Here we prove subnormal counterparts of the well-known…

Variational calculus with constraints on general algebroids

Energy Technology Data Exchange (ETDEWEB)

Grabowska, Katarzyna [Physics Department, Division of Mathematical Methods in Physics, University of Warsaw, Hoza 69, 00-681 Warszawa (Poland); Grabowski, Janusz [Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, PO Box 21, 00-956 Warszawa (Poland)], E-mail: konieczn@fuw.edu.pl, E-mail: jagrab@impan.gov.pl

2008-05-02

Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and geometrical settings. The constrained Euler-Lagrange equations are derived for analogs of holonomic, vakonomic and nonholonomic constraints. This general model covers the majority of first-order Lagrangian systems which are present in the literature and reduces to the standard variational calculus and the Euler-Lagrange equations in classical mechanics for E = TM.

Variational calculus with constraints on general algebroids

International Nuclear Information System (INIS)

Grabowska, Katarzyna; Grabowski, Janusz

2008-01-01

Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and geometrical settings. The constrained Euler-Lagrange equations are derived for analogs of holonomic, vakonomic and nonholonomic constraints. This general model covers the majority of first-order Lagrangian systems which are present in the literature and reduces to the standard variational calculus and the Euler-Lagrange equations in classical mechanics for E = TM

A sequent calculus for signed interval logic

DEFF Research Database (Denmark)

Rasmussen, Thomas Marthedal

2001-01-01

We propose and discuss a complete sequent calculus formulation for Signed Interval Logic (SIL) with the chief purpose of improving proof support for SIL in practice. The main theoretical result is a simple characterization of the limit between decidability and undecidability of quantifier-free SIL....... We present a mechanization of SIL in the generic proof assistant Isabelle and consider techniques for automated reasoning. Many of the results and ideas of this report are also applicable to traditional (non-signed) interval logic and, hence, to Duration Calculus....

Modular invariance and covariant loop calculus

International Nuclear Information System (INIS)

Petersen, J.L.; Roland, K.O.; Sidenius, J.R.

1988-01-01

The covariant loop calculus provides an efficient technique for computing explicit expressions for the density on moduli space corresponding to arbitrary (bosonic string) loop diagrams. Since modular invariance is not manifest, however, we carry out a detailed comparison with known explicit two- and three-loop results derived using analytic geometry (one loop is known to be okay). We establish identity to 'high' order in some moduli and exactly in others. Agreement is found as a result of various nontrivial cancellations, in part related to number theory. We feel our results provide very strong support for the correctness of the covariant loop calculus approach. (orig.)

Modular invariance and covariant loop calculus

International Nuclear Information System (INIS)

Petersen, J.L.; Roland, K.O.; Sidenius, J.R.

1988-01-01

The covariant loop calculus provides and efficient technique for computing explicit expressions for the density on moduli space corresponding to arbitrary (bosonic string) loop diagrams. Since modular invariance is not manifest, however, we carry out a detailed comparison with known explicit 2- and 3- loop results derived using analytic geometry (1 loop is known to be ok). We establish identity to 'high' order in some moduli and exactly in others. Agreement is found as a result of various non-trivial cancellations, in part related to number theory. We feel our results provide very strong support for the correctness of the covariant loop calculus approach. (orig.)

Model Checking Processes Specified In Join-Calculus Algebra

Directory of Open Access Journals (Sweden)

Sławomir Piotr Maludziński

2014-01-01

Full Text Available This article presents a model checking tool used to verify concurrent systems specified in join-calculus algebra. The temporal properties of systems under verification are expressed in CTL logic. Join-calculus algebra with its operational semantics defined by the chemical abstract machine serves as the basic method for the specification of concurrent systems and their synchronization mechanisms, and allows the examination of more complex systems.

A comparison of dental ultrasonic technologies on subgingival calculus removal: a pilot study.

Science.gov (United States)

Silva, Lidia Brión; Hodges, Kathleen O; Calley, Kristin Hamman; Seikel, John A

2012-01-01

This pilot study compared the clinical endpoints of the magnetostrictive and piezoelectric ultrasonic instruments on calculus removal. The null hypothesis stated that there is no statistically significant difference in calculus removal between the 2 instruments. A quasi-experimental pre- and post-test design was used. Eighteen participants were included. The magnetostrictive and piezoelectric ultrasonic instruments were used in 2 assigned contra-lateral quadrants on each participant. A data collector, blind to treatment assignment, assessed the calculus on 6 predetermined tooth sites before and after ultrasonic instrumentation. Calculus size was evaluated using ordinal measurements on a 4 point scale (0, 1, 2, 3). Subjects were required to have size 2 or 3 calculus deposit on the 6 predetermined sites. One clinician instrumented the pre-assigned quadrants. A maximum time of 20 minutes of instrumentation was allowed with each technology. Immediately after instrumentation, the data collector then conducted the post-test calculus evaluation. The repeated analysis of variance (ANOVA) was used to analyze the pre- and post-test calculus data (p≤0.05). The null hypothesis was accepted indicating that there is no statistically significant difference in calculus removal when comparing technologies (p≤0.05). Therefore, under similar conditions, both technologies removed the same amount of calculus. This research design could be used as a foundation for continued research in this field. Future studies include implementing this study design with a larger sample size and/or modifying the study design to include multiple clinicians who are data collectors. Also, deposit removal with periodontal maintenance patients could be explored.

Differential calculus and its applications

CERN Document Server

Field, Michael J

2013-01-01

Based on undergraduate courses in advanced calculus, the treatment covers a wide range of topics, from soft functional analysis and finite-dimensional linear algebra to differential equations on submanifolds of Euclidean space. 1976 edition.

Dental calculus is associated with death from heart infarction.

Science.gov (United States)

Söder, Birgitta; Meurman, Jukka H; Söder, Per-Östen

2014-01-01

We studied whether the amount of dental calculus is associated with death from heart infarction in the dental infection-atherosclerosis paradigm. Participants were 1676 healthy young Swedes followed up from 1985 to 2011. At the beginning of the study all subjects underwent oral clinical examination including dental calculus registration scored with calculus index (CI). Outcome measure was cause of death classified according to WHO International Classification of Diseases. Unpaired t-test, Chi-square tests, and multiple logistic regressions were used. Of the 1676 participants, 2.8% had died during follow-up. Women died at a mean age of 61.5 years and men at 61.7 years. The difference in the CI index score between the survivors versus deceased patients was significant by the year 2009 (P dental visits, dental plaque, periodontal pockets, education, income, socioeconomic status, and pack-years of smoking, CI score appeared to be associated with 2.3 times the odds ratio for cardiac death. The results confirmed our study hypothesis by showing that dental calculus indeed associated statistically with cardiac death due to infarction.

On Functional Calculus Estimates

NARCIS (Netherlands)

Schwenninger, F.L.

2015-01-01

This thesis presents various results within the field of operator theory that are formulated in estimates for functional calculi. Functional calculus is the general concept of defining operators of the form $f(A)$, where f is a function and $A$ is an operator, typically on a Banach space. Norm

Stochastic Pi-calculus Revisited

DEFF Research Database (Denmark)

Cardelli, Luca; Mardare, Radu Iulian

2013-01-01

We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of...

Regge trajectories and Hagedorn behavior: Hadronic realizations of dynamical dark matter

Science.gov (United States)

Dienes, Keith R.; Huang, Fei; Su, Shufang; Thomas, Brooks

2017-11-01

Dynamical Dark Matter (DDM) is an alternative framework for dark-matter physics in which the dark sector comprises a vast ensemble of particle species whose Standard-Model decay widths are balanced against their cosmological abundances. In this talk, we study the properties of a hitherto-unexplored class of DDM ensembles in which the ensemble constituents are the "hadronic" resonances associated with the confining phase of a strongly-coupled dark sector. Such ensembles exhibit masses lying along Regge trajectories and Hagedorn-like densities of states that grow exponentially with mass. We investigate the applicable constraints on such dark-"hadronic" DDM ensembles and find that these constraints permit a broad range of mass and confinement scales for these ensembles. We also find that the distribution of the total present-day abundance across the ensemble is highly correlated with the values of these scales. This talk reports on research originally presented in Ref. [1].

Extending the Extensional Lambda Calculus with Surjective Pairing is Conservative

DEFF Research Database (Denmark)

Støvring, Kristian

2006-01-01

We answer Klop and de Vrijer's question whether adding surjective-pairing axioms to the extensional lambda calculus yields a conservative extension. The answer is positive. As a byproduct we obtain a "syntactic" proof that the extensional lambda calculus with surjective pairing is consistent....

Double Regge pole exchange model analysis of a 7 Gev/c. pi. /sup -/p experiment. [Absolute cross sections, one-particle exchange, diffraction scattering

Energy Technology Data Exchange (ETDEWEB)

Chao, A C.L.

1973-01-01

A double Regge Pole Exchange Model is used to analyze Quasi-Three-Body final states selected from a 7 GeV/c - /sup -/p experiment. Three sets of data are analyzed namely: I ..pi../sup -/p ..-->.. p..pi../sup +/..pi../sup -/..pi../sup -/; II ..pi../sup -/p ..-->.. p..pi../sup +/..pi../sup -/..pi../sup -/..pi../sup 0/; III ..pi../sup -/p ..-->.. ..pi../sup +/..pi../sup +/..pi../sup -/..pi../sup -/n. The final states, selected from data sets I, II and III are (rho/sup 0/..pi../sup -/p, f/sup 0/..pi../sup -/p, ..pi../sup -/..pi../sup -/..delta../sup + +/), (rho/sup 0/..pi../sup -/..delta../sup +/, rho/sup -/..pi..-..delta../sup + +/, ..omega pi../sup -/p) and (rho/sup 0/..pi../sup -/..delta../sup +/), respectively. It is found that these channels after appropriate kinematic cuts can be well described by exchanging two Regge Trajectories. Predictions for the absolute cross-sections were also obtained by taking limits of one particle exchange and a diffraction scattering approximation. (auth)

Advanced calculus

CERN Document Server

Fitzpatrick, Patrick M

2009-01-01

Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclide

Matrix calculus

CERN Document Server

Bodewig, E

1959-01-01

Matrix Calculus, Second Revised and Enlarged Edition focuses on systematic calculation with the building blocks of a matrix and rows and columns, shunning the use of individual elements. The publication first offers information on vectors, matrices, further applications, measures of the magnitude of a matrix, and forms. The text then examines eigenvalues and exact solutions, including the characteristic equation, eigenrows, extremum properties of the eigenvalues, bounds for the eigenvalues, elementary divisors, and bounds for the determinant. The text ponders on approximate solutions, as well

Giant urinary bladder calculus: Case report | Otieno | East African ...

African Journals Online (AJOL)

A vertical calculus weighing more than 100 g is categorised as a giant urinary bladder stone. Giant urinary bladder stones are very rare and very few cases have been reported in English literature and only one case from Africa. This is a case report of a patient with a giant urinary bladder calculus presenting as a rectal ...

Effects of Clicker Use on Calculus Students' Mathematics Anxiety

Science.gov (United States)

Batchelor, John

2015-01-01

This paper reports the results of a survey study of clicker use and mathematics anxiety among students enrolled in an undergraduate calculus course during the Fall 2013 semester. Students in two large lecture sections of calculus completed surveys at the beginning and end of the course. One class used clickers, whereas the other class was taught…

Covariant differential calculus on quantum spheres of odd dimension

International Nuclear Information System (INIS)

Welk, M.

1998-01-01

Covariant differential calculus on the quantum spheres S q 2N-1 is studied. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the quantum spheres, a framework of covariant differential calculus is established, including first and higher order calculi and a symmetry concept. (author)

Projects for calculus the language of change

CERN Document Server

Stroyan, Keith D

1999-01-01

Projects for Calculus is designed to add depth and meaning to any calculus course. The fifty-two projects presented in this text offer the opportunity to expand the use and understanding of mathematics. The wide range of topics will appeal to both instructors and students. Shorter, less demanding projects can be managed by the independent learner, while more involved, in-depth projects may be used for group learning. Each task draws on special mathematical topics and applications from subjects including medicine, engineering, economics, ecology, physics, and biology.Subjects including:* Medicine* Engineering* Economics* Ecology* Physics* Biology

Data Quality Indicators Composition and Calculus: Engineering and Information Systems Approaches

Directory of Open Access Journals (Sweden)

Leon REZNIK

2015-02-01

Full Text Available Big Data phenomenon is a result of novel technological developments in sensor, computer and communication technologies. Nowadays more and more data are produced by nanoscale photonic, optoelectronic and electronic devices. However, their quality characteristics could be very low. The paper proposes new methods of the data management with huge data amounts that is based on associating of data quality indicators with each data entity. To achieve this goal, one needs to define the composition of the data quality indicators and to develop their integration calculus. As data quality evaluation involves multi-disciplinary research, various metrics have been investigated. The paper describes two major approaches in assigning the data quality indicators and developing their integration calculus. The information systems approach employs traditional high-level metrics like data accuracy, consistency and completeness. The engineering approach utilizes signal characteristics processed with the probability based calculus. The data quality metrics composition and calculus are discussed. The tools developed to automate the metrics selection and calculus procedures are presented. The user- friendly interface examples are provided.

Quantifying calculus: a suggested new approach for recording an important indicator of diet and dental health.

Science.gov (United States)

Greene, T R; Kuba, C L; Irish, J D

2005-01-01

This paper describes a quantitative approach to the assessment of dental calculus in human archaeological skeletal samples. The approach combines the ranked calculus scoring method described by Buikstra and Ubelaker [1994. Arkansas Archeological Survey Research Series, Arkansas Archeological Survey, Fayetteville, Arkansas] and a modified Simplified Calculus Index, utilized by dental clinicians. We recorded amounts of calculus on the buccal, lingual, and interproximal surface of all extant teeth, and generated an index for the maxillary posterior dentition, maxillary anterior dentition, mandibular posterior dentition, and mandibular anterior dentition for three skeletal samples. They include 145 Egyptian Predynastic individuals from the site of Hierakonpolis, 104 Predynastic individuals from Naqada, Egypt, and 101 Meroitic Nubians from Semna South, present-day Sudan. Mann-Whitney U tests were used to analyze differences between the sexes and among age groups at each site. The results demonstrate that the calculus indices more effectively reveal trends and differences in calculus severity than frequency data can alone. For example, at Hierakonpolis, males (18-35 years) had significantly more calculus in the maxillary posterior dentition than females, while females (50+ years) had significantly more calculus in the maxillary posterior teeth. Frequency data merely showed that 94% of both males and females had calculus. The use of calculus indices can reveal how quickly calculus accumulates with age within the dental arcade and within a sample. Moreover, better understanding of the severity and location of calculus can improve a researcher's knowledge regarding the effect of calculus on dental pathologies, such as carious lesions and periodontal disease.

On the Expressive Power of Polyadic Synchronisation in π- calculus

DEFF Research Database (Denmark)

Carbone, Marco; Maffeis, Sergio

2002-01-01

We extend the pi-calculus with polyadic synchronisation, a generalisation of the communication mechanism which allows channel names to be composite. We show that this operator embeds nicely in the theory of pi-calculus, we suggest that it permits divergence-free encodings of distributed calculi, ...

Duration Calculus: Logical Foundations

DEFF Research Database (Denmark)

Hansen, Michael Reichhardt; Chaochen, Zhou

1997-01-01

The Duration Calculus (abbreviated DC) represents a logical approach to formal design of real-time systems, where real numbers are used to model time and Boolean valued functions over time are used to model states and events of real-time systems. Since it introduction, DC has been applied to many...

Provability Calculus of Constructions

DEFF Research Database (Denmark)

Nyblad, Kasten

This thesis presents a type system, Provability Calculus of Constructions (PCoC) that can be used for the formalization of logic. In a theorem prover based on the system, the user can extend the prover with new inference rules in a logically consistent manner. This is done by representing PCo...