scholarly journals A General Scheme for Information Interception in the Ping-Pong Protocol

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Piotr Zawadzki ◽  
Jarosław Adam Miszczak
Keyword(s):  
General Scheme ◽  
Vacuum State ◽  
Theoretical Background ◽  
Explicit Scheme ◽  
Previous Approach ◽  
Quantum Direct Communication ◽  
Communication Paradigm ◽  
Higher Dimensional ◽  
Ping Pong ◽  
Special Cases

The existence of undetectable eavesdropping of dense coded information has been already demonstrated by Pavičić for the quantum direct communication based on the ping-pong paradigm. However, (a) the explicit scheme of the circuit is only given and no design rules are provided; (b) the existence of losses is implicitly assumed; (c) the attack has been formulated against qubit based protocol only and it is not clear whether it can be adapted to higher dimensional systems. These deficiencies are removed in the presented contribution. A new generic eavesdropping scheme built on a firm theoretical background is proposed. In contrast to the previous approach, it does not refer to the properties of the vacuum state, so it is fully consistent with the absence of losses assumption. Moreover, the scheme applies to the communication paradigm based on signal particles of any dimensionality. It is also shown that some well known attacks are special cases of the proposed scheme.

scholarly journals On Reay's Relaxed Tverberg Conjecture and Generalizations of Conway's Thrackle Conjecture

10.37236/6516 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Megumi Asada ◽  
Ryan Chen ◽  
Florian Frick ◽  
Frederick Huang ◽  
Maxwell Polevy ◽  
...  
Keyword(s):  
Geometric Property ◽  
Convex Sets ◽  
Convex Hulls ◽  
Open Problems ◽  
Higher Dimensional ◽  
Special Cases ◽  
Minimum Number ◽  
Point Set ◽  
Colored Version ◽  
Special Case

Reay's relaxed Tverberg conjecture and Conway's thrackle conjecture are open problems about the geometry of pairwise intersections. Reay asked for the minimum number of points in Euclidean $d$-space that guarantees any such point set admits a partition into $r$ parts, any $k$ of whose convex hulls intersect. Here we give new and improved lower bounds for this number, which Reay conjectured to be independent of $k$. We prove a colored version of Reay's conjecture for $k$ sufficiently large, but nevertheless $k$ independent of dimension $d$. Pairwise intersecting convex hulls have severely restricted combinatorics. This is a higher-dimensional analogue of Conway's thrackle conjecture or its linear special case. We thus study convex-geometric and higher-dimensional analogues of the thrackle conjecture alongside Reay's problem and conjecture (and prove in two special cases) that the number of convex sets in the plane is bounded by the total number of vertices they involve whenever there exists a transversal set for their pairwise intersections. We thus isolate a geometric property that leads to bounds as in the thrackle conjecture. We also establish tight bounds for the number of facets of higher-dimensional analogues of linear thrackles and conjecture their continuous generalizations.

Electronic wave functions IV. Some general theorems for the calculation of Schrödinger integrals between complicated vector-coupled functions for many-electron atoms

1951 ◽  
Vol 207 (1089) ◽  
pp. 181-197 ◽  
Keyword(s):  
General Scheme ◽  
Wave Functions ◽  
Important Class ◽  
Atomic Spectra ◽  
Electronic Wave ◽  
Special Cases ◽  
Reduction Methods ◽  
Electronic Wave Functions

A scheme of theorems is developed which enables an important class of integrals of the Schrödinger Hamiltonian between antisymmetric vector-coupled functions of the Russell-Saunders type to be expressed in terms of integrals corresponding to smaller numbers of electrons. These integrals form the most important class occurring in problems of atomic spectra and the structure of atoms, but only particular reduction methods have been available previously. The analysis is based on the usual commutation properties of the angular operators, but some new formal rearrangements of the couplings within integrals are made, which give the essential reduction relations. The expansions are in terms of certain coefficients denoted by V and W , which must be evaluated numerically, but the particular values of which can be used repeatedly for unlimited numbers of special cases. These relations provide an important part of a general scheme of reduction of all Schrödinger integrals.

Parametric and Topological Control in Shape Optimization

2006 ◽  
Author(s):  
Jiaqin Chen ◽  
Vadim Shapiro ◽  
Krishnan Suresh ◽  
Igor Tsukanov
Keyword(s):  
Shape Optimization ◽  
Optimization Techniques ◽  
Free Form ◽  
Large Space ◽  
Design And Optimization ◽  
B Splines ◽  
Novel Approach ◽  
Higher Dimensional ◽  
Special Cases ◽  
R Functions

We propose a novel approach to shape optimization that combines and retains the advantages of the earlier optimization techniques. The shapes in the design space are represented implicitly as level sets of a higher-dimensional function that is constructed using B-splines (to allow free-form deformations), and parameterized primitives combined with R-functions (to support desired parametric changes). Our approach to shape design and optimization offers great flexibility because it provides explicit parametric control of geometry and topology within a large space of freeform shapes. The resulting method is also general in that it subsumes most other types of shape optimization as special cases. We describe an implementation of the proposed technique with attractive numerical properties. The effectiveness of the method is demonstrated by several numerical examples.

scholarly journals Torsion points and height jumping in higher-dimensional families of abelian varieties

2019 ◽  
Vol 15 (09) ◽  
pp. 1801-1826 ◽  
Author(s):  
David Holmes
Keyword(s):  
Infinite Order ◽  
Abelian Varieties ◽  
Uniform Boundedness ◽  
Torsion Points ◽  
Small Height ◽  
Higher Dimensional ◽  
Special Cases ◽  
Set Of Points

In 1983, Silverman and Tate showed that the set of points in a 1-dimensional family of abelian varieties where a section of infinite order has “small height” is finite. We conjecture a generalization to higher-dimensional families, where we replace “finite” by “not Zariski dense.” We show that this conjecture would imply the uniform boundedness conjecture for torsion points on abelian varieties. We then prove a few special cases of this new conjecture.

Numerical Scheme for Generalized Isoparametric Constraint Variational Problems With A-Operator

2013 ◽  
Author(s):  
Rajesh K. Pandey ◽  
Om P. Agrawal
Keyword(s):  
Numerical Scheme ◽  
Fractional Derivatives ◽  
Dimensional Space ◽  
General Scheme ◽  
Functional Space ◽  
Approximate Solutions ◽  
Variational Problems ◽  
Approximation Schemes ◽  
Finite Dimensional Space ◽  
Special Cases

This paper presents a numerical scheme for a class of Isoperimetric Constraint Variational Problems (ICVPs) defined in terms of an A-operator introduced recently. In this scheme, Bernstein’s polynomials are used to approximate the desired function and to reduce the problem from a functional space to an eigenvalue problem in a finite dimensional space. Properties of the eigenvalues and eigenvectors of this problem are used to obtain approximate solutions to the problem. Results for two examples are presented to demonstrate the effectiveness of the proposed scheme. In special cases the A-operator reduce to Riemann-Liouville, Caputo, Riesz-Riemann-Liouville and Riesz-Caputo, and several other fractional derivatives defined in the literature. Thus, the approach presented here provides a general scheme for ICVPs defined using different types of fractional derivatives. Although, only Bernstein’s polynomials are used here to approximate the solutions, many other approximation schemes are possible. Effectiveness of these approximation schemes will be presented in the future.

scholarly journals Subdivision Depth Computation for Tensor Productn-Ary Volumetric Models

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Ghulam Mustafa ◽  
Muhammad Sadiq Hashmi
Keyword(s):  
Tensor Product ◽  
Error Bounds ◽  
Error Control ◽  
Computational Formula ◽  
Evaluation Technique ◽  
Volumetric Models ◽  
Higher Dimensional ◽  
Special Cases ◽  
Subdivision Depth ◽  
Control Tool

We offer computational formula of subdivision depth for tensor productn-ary (n⩾2) volumetric models based on error bound evaluation technique. This formula provides and error control tool in subdivision schemes over regular hexahedron lattice in higher-dimensional spaces. Moreover, the error bounds of Mustafa et al. (2006) are special cases of our bounds.

scholarly journals The Manin constant in the semistable case

2018 ◽  
Vol 154 (9) ◽  
pp. 1889-1920 ◽  
Author(s):  
Kęstutis Česnavičius
Keyword(s):  
Vector Space ◽  
Elliptic Curve ◽  
Abelian Varieties ◽  
Higher Dimensional ◽  
Special Cases ◽  
Modular Parametrization ◽  
De Rham ◽  
Neron Models ◽  
General Relations ◽  
Néron Models

For an optimal modular parametrization $J_{0}(n){\twoheadrightarrow}E$ of an elliptic curve $E$ over $\mathbb{Q}$ of conductor $n$, Manin conjectured the agreement of two natural $\mathbb{Z}$-lattices in the $\mathbb{Q}$-vector space $H^{0}(E,\unicode[STIX]{x1D6FA}^{1})$. Multiple authors generalized his conjecture to higher-dimensional newform quotients. We prove the Manin conjecture for semistable $E$, give counterexamples to all the proposed generalizations, and prove several semistable special cases of these generalizations. The proofs establish general relations between the integral $p$-adic étale and de Rham cohomologies of abelian varieties over $p$-adic fields and exhibit a new exactness result for Néron models.

Linear configurations of complete graphs K4 and K5 in ℝ3, and higher dimensional analogs

2017 ◽  
Vol 26 (05) ◽  
pp. 1750028
Author(s):  
Andrew Marshall
Keyword(s):  
Fundamental Group ◽  
Symmetric Group ◽  
Configuration Space ◽  
Braid Group ◽  
Simplicial Complexes ◽  
Alternating Group ◽  
Complete Graphs ◽  
Mapping Cylinder ◽  
Higher Dimensional ◽  
Special Cases

We investigate the space [Formula: see text] of images of linearly embedded finite simplicial complexes in [Formula: see text] isomorphic to a given complex [Formula: see text], focusing on two special cases: [Formula: see text] is the [Formula: see text]-skeleton [Formula: see text] of an [Formula: see text]-simplex, and [Formula: see text] is the [Formula: see text]-skeleton [Formula: see text] of an [Formula: see text]-simplex, so [Formula: see text] has codimension 2 in [Formula: see text], in both cases. The main result is that for [Formula: see text], [Formula: see text] (for either [Formula: see text]) deformation retracts to a subspace homeomorphic to the double mapping cylinder [Formula: see text] where [Formula: see text] is the alternating group and [Formula: see text] the symmetric group. The resulting fundamental group provides an example of a generalization of the braid group, which is the fundamental group of the configuration space of points in the plane.

scholarly journals Classical and quantum dynamics of higher-derivative systems

2017 ◽  
Vol 32 (33) ◽  
pp. 1730025 ◽  
Author(s):  
Andrei Smilga
Keyword(s):  
Field Theory ◽  
Classical Solution ◽  
Ground State ◽  
Quantum Dynamics ◽  
Higher Derivative ◽  
Higher Dimensional ◽  
Special Cases ◽  
Theory Of Everything ◽  
Higher Derivatives

A brief review of the physics of systems including higher derivatives in the Lagrangian is given. All such systems involve ghosts, i.e. the spectrum of the Hamiltonian is not bounded from below and the vacuum ground state is absent. Usually, this leads to collapse and loss of unitarity. In certain special cases, this does not happen, however, ghosts are benign. We speculate that the Theory of Everything is a higher-derivative field theory, characterized by the presence of such benign ghosts and defined in a higher-dimensional bulk. Our Universe then represents a classical solution in this theory, having the form of a 3-brane embedded in the bulk.

scholarly journals Variational methods for boundary value problems

2000 ◽  
Vol 4 (2) ◽  
pp. 193-204
Author(s):  
B. Tsang ◽  
S. W. Taylor ◽  
G. C. Wake
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Point Of View ◽  
One Dimension ◽  
Computational Point ◽  
Higher Dimensional ◽  
Special Cases ◽  
Variational Form ◽  
General Boundary Value Problem

The variational formulation of boundary value problems is valuable in providing remarkably easy computational algorithms as well as an alternative framework with which to prove existence results. Boundary conditions impose constraints which can be annoying from a computational point of view. The question is then posed: what is the most general boundary value problem which can be posed in variational form with the boundary conditions appearing naturally? Special cases of two-point problems in one-dimension and some higher dimensional problems are addressed. There is a deep connection with self-adjointness for the linear case. Further cases under which a Lagrangian may or may not exist are explained.

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