Discovering Injective Mapping Between Relations in Astrophysics Databases

PARIKH MATRICES, AMIABILITY AND ISTRAIL MORPHISM

International Journal of Foundations of Computer Science ◽

10.1142/s0129054110007702 ◽

2010 ◽

Vol 21 (06) ◽

pp. 1021-1033 ◽

Cited By ~ 6

Author(s):

ADRIAN ATANASIU

Keyword(s):

Injective Mapping ◽

Additional Information ◽

Binary Case ◽

Matrix Mapping

Using the fact that the Parikh matrix mapping is not an injective mapping, the paper investigates some properties of the set of words having the same Parikh matrix; these words are called "amiable" or "M - equivalent". The presented paper uses the results obtained in [3] for the binary case. The aim is to distinguish the amiable words by using a morphism that provides additional information about them. The morphism proposed here is the Istrail morphism.

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The fundamental theorems of affine and projective geometry revisited

Communications in Contemporary Mathematics ◽

10.1142/s0219199716500590 ◽

2016 ◽

Vol 19 (05) ◽

pp. 1650059

Author(s):

Shiri Artstein-Avidan ◽

Boaz A. Slomka

Keyword(s):

Three Dimensional ◽

Real Space ◽

Vector Spaces ◽

Real Vector ◽

Injective Mapping ◽

Finite Dimensional ◽

Fixed Set ◽

Dimensional Projective Space ◽

Projective Lines ◽

Fundamental Theorems

The fundamental theorem of affine geometry is a classical and useful result. For finite-dimensional real vector spaces, the theorem roughly states that a bijective self-mapping which maps lines to lines is affine-linear. In this paper, we prove several generalizations of this result and of its classical projective counterpart. We show that under a significant geometric relaxation of the hypotheses, namely that only lines parallel to one of a fixed set of finitely many directions are mapped to lines, an injective mapping of the space must be of a very restricted polynomial form. We also prove that under mild additional conditions the mapping is forced to be affine-additive or affine-linear. For example, we show that five directions in three-dimensional real space suffice to conclude affine-additivity. In the projective setting, we show that [Formula: see text] fixed projective points in real [Formula: see text]-dimensional projective space, through which all projective lines that pass are mapped to projective lines, suffice to conclude projective-linearity.

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Orthogonal labeling

Indonesian Journal of Combinatorics ◽

10.19184/ijc.2016.1.1.1 ◽

2016 ◽

Vol 1 (1) ◽

pp. 1

Author(s):

Bernard Immanuel ◽

Kiki A. Sugeng

Keyword(s):

Euclidean Space ◽

Early Result ◽

Algebraic Structure ◽

Connected Graph ◽

Maximum Degree ◽

Injective Mapping ◽

Distance Magic Labeling ◽

Harmonious Labeling ◽

Simple Connected Graph ◽

Cycle Graph

<div class="page" title="Page 1"><div class="layoutArea"><div class="column">Let ∆G be the maximum degree of a simple connected graph G(V,E). An injective mapping P : V → R∆G is said to be an orthogonal labeling of G if uv,uw ∈ E implying (P(v) − P(u)) · (P(w) − P(u)) = 0, where · is the usual dot product defined in Euclidean space. A graph G which has an orthogonal labeling is called an orthogonal graph. This labeling is motivated by the existence of several labelings defined by some algebraic structure, i.e. harmonious labeling and group distance magic labeling. In this paper we study some preliminary results on orthogonal labeling. One of the early result is the fact that cycle graph with even vertices are orthogonal, while ones with odd vertices are not. The main results in this paper state that any graph containing K3 as its subgraph is non-orthogonal and that a graph G′ obtained from adding a pendant to a vertex in orthogonal graph G is orthogonal. In the end of the paper we state the corollary that any tree is orthogonal. </div></div></div>

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Injective Mapping in Observer Error Linearization

IFAC Proceedings Volumes ◽

10.1016/s1474-6670(17)35295-3 ◽

2001 ◽

Vol 34 (6) ◽

pp. 903-908

Author(s):

M. Hou ◽

A. Banaszuk

Keyword(s):

Observer Error ◽

Injective Mapping

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Minimal Reversible Deterministic Finite Automata

International Journal of Foundations of Computer Science ◽

10.1142/s0129054118400063 ◽

2018 ◽

Vol 29 (02) ◽

pp. 251-270 ◽

Cited By ~ 4

Author(s):

Markus Holzer ◽

Sebastian Jakobi ◽

Martin Kutrib

Keyword(s):

Lower Bounds ◽

Finite Automata ◽

Transition Function ◽

Upper And Lower Bounds ◽

State Graph ◽

Deterministic Finite Automata ◽

Injective Mapping ◽

Pattern Approach ◽

Almost All

We study reversible deterministic finite automata (REV-DFAs), that are partial deterministic finite automata whose transition function induces an injective mapping on the state set for every letter of the input alphabet. We give a structural characterization of regular languages that can be accepted by REV-DFAs. This characterization is based on the absence of a forbidden pattern in the (minimal) deterministic state graph. Again with a forbidden pattern approach, we also show that the minimality of REV-DFAs among all equivalent REV-DFAs can be decided. Both forbidden pattern characterizations give rise to [Formula: see text]-complete decision algorithms. In fact, our techniques allow us to construct the minimal REV-DFA for a given minimal DFA. These considerations lead to asymptotic upper and lower bounds on the conversion from DFAs to REV-DFAs. Thus, almost all problems that concern uniqueness and the size of minimal REV-DFAs are solved.

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Reliability of Complex Structures by Large Admissible Perturbations

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.2920109 ◽

1993 ◽

Vol 115 (3) ◽

pp. 167-178 ◽

Cited By ~ 7

Author(s):

E. Beyko ◽

M. M. Bernitsas

Keyword(s):

Finite Elements ◽

Normal Modes ◽

Failure Surface ◽

Threshold Value ◽

Path Selection ◽

Perturbation Approach ◽

Load Path ◽

Injective Mapping ◽

Analysis And Design ◽

The Individual

The perturbation approach to reliability (PAR) is a powerful methodology for reliability analysis and design of large structures. Its main features are: F1) PAR provides the exact global failure equation for any failure criterion for which the corresponding structural analysis can be performed by finite elements. F2) Geometry, material, and loads appear explicitly in the global failure equations and are treated as random variables. No need arises for load path selection or load pattern specification. F3) PAR introduces an invariant and consistent redundancy definition as an injective mapping restricted on the failure surface. Thus, the redundancy/reliability of the structure is expressed in terms of the redundancy/reliability of its structural components. F4) The norm of the Rosenblatt transformed reliability injection is the reliability index. F5) For each global failure equation or combination of failure equations, PAR computes the individual or joint design points without enumerating paths to failure, trial and error, or repeated finite element analyses. F6) Serviceability or ultimate global structural failure is defined by specifying a threshold value of any quantity that can be computed by finite elements: natural frequencies, dynamic normal modes, static deflections, static stresses, buckling loads, and buckling modes are implemented in PAR. Stress failure equations are used along with linearized plasticity surfaces to identify element failure. Several applications are presented to assess PAR.

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Boolean functions as points on the hypersphere in the Euclidean space

Discrete Mathematics and Applications ◽

10.1515/dma-2019-0009 ◽

2019 ◽

Vol 29 (2) ◽

pp. 89-101 ◽

Cited By ~ 2

Author(s):

Oleg A. Logachev ◽

Sergey N. Fedorov ◽

Valerii V. Yashchenko

Keyword(s):

Euclidean Space ◽

Boolean Function ◽

Boolean Functions ◽

Nonlinear Functions ◽

New Approach ◽

Injective Mapping

Abstract A new approach to the study of algebraic, combinatorial, and cryptographic properties of Boolean functions is proposed. New relations between functions have been revealed by consideration of an injective mapping of the set of Boolean functions onto the sphere in a Euclidean space. Moreover, under this mapping some classes of functions have extremely regular localizations on the sphere. We introduce the concept of curvature of a Boolean function, which characterizes its proximity (in some sense) to maximally nonlinear functions.

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BINARY AMIABLE WORDS

International Journal of Foundations of Computer Science ◽

10.1142/s0129054107004735 ◽

2007 ◽

Vol 18 (02) ◽

pp. 387-400 ◽

Cited By ~ 30

Author(s):

ADRIAN ATANASIU

Keyword(s):

Equivalence Class ◽

Characterization Theorem ◽

Equivalence Classes ◽

Rank Distance ◽

Injective Mapping ◽

Basic Properties ◽

Matrix Mapping

Using the fact that the Parikh matrix mapping is not an injective mapping, the paper investigates some properties of the set of the binary words having the same Parikh matrix; these words are called "amiable" Some results concerning the conditions when the equivalence classes of amiable words have more than one element, a characterization theorem concerning a graph associated to an equivalence class of amiable words, and some basic properties of a rank distance defined on these classes are the main subjects considered here.

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Systems of knowledge representation based on stratified graphs. Application in Natural Language Generation

Carpathian Journal of Mathematics ◽

10.37193/cjm.2016.01.05 ◽

2016 ◽

Vol 32 (1) ◽

pp. 49-62

Author(s):

DANIELA DANCIULESCU ◽

◽

MIHAELA COLHON ◽

◽

Keyword(s):

Knowledge Representation ◽

Natural Language ◽

Natural Language Generation ◽

Inference Process ◽

Knowledge Processing ◽

Language Generation ◽

Universal Algebras ◽

Injective Mapping ◽

Regular Path ◽

Real Objects

The concept of stratified graph introduces some method of knowledge representation (see [T¸ and ˘ areanu, N., ˘ Knowledge representation by labeled stratified graphs, Proc. 8th World Multi-Conference on Systemics, Cybernetics and Informatics, 5 (2004), 345–350; T¸ and ˘ areanu, N., ˘ Proving the Existence of Labelled Stratified Graphs, An. Univ. Craiova Ser. Mat. Inform., 27 (2000), 81–92]) The inference process developed for this method uses the paths of the stratified graphs, an order between the elementary arcs of a path and some results of universal algebras. The order is defined by considering a structured path instead of a regular path. In this paper we define the concept of system of knowledge representation as a tuple of the following components: a stratified graph G, a partial algebra Y of real objects, an embedding mapping (an injective mapping that embeds the nodes of G into objects of Y ) and a set of algorithms such that each of them can combine two objects of Y to get some other object of Y . We define also the concept of inference process performed by a system of knowledge processing in which the interpretation of the symbolic elements is defined by means of natural language constructions. In this manner we obtained a mechanism for texts generation in a natural language (for this approach, Romanian).

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Ripplet transform and its extension to Boehmians

Georgian Mathematical Journal ◽

10.1515/gmj-2017-0056 ◽

2020 ◽

Vol 27 (1) ◽

pp. 149-156

Author(s):

Rajakumar Roopkumar

Keyword(s):

Convolution Theorem ◽

Continuous Linear ◽

Inversion Theorem ◽

Ripplet Transform ◽

Injective Mapping

AbstractFirst, we correct the mistake in the inversion theorem of the ripplet transform in the literature. Next, we prove a convolution theorem for the ripplet transform and extend the ripplet transform as a continuous, linear, injective mapping from a suitable Boehmian space into another Boehmian space.

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