scholarly journals Unary Self-verifying Symmetric Difference Automata

2016 ◽  
pp. 180-191 ◽  
Author(s):  
Laurette Marais ◽  
Lynette van Zijl
Keyword(s):  
Symmetric Difference

scholarly journals A theorem on connected graphs in which every edge belongs to a 1-factor

1974 ◽  
Vol 18 (4) ◽  
pp. 450-452 ◽  
Author(s):  
Charles H. C. Little
Keyword(s):  
Symmetric Difference ◽  
Connected Graphs

In this paper, we consider factor covered graphs, which are defined basically as connected graphs in which every edge belongs to a 1-factor. The main theorem is that for any two edges e and e′ of a factor covered graph, there is a cycle C passing through e and e′ such that the edge set of C is the symmetric difference of two 1-factors.

THE WIENER INDEX OF DISJUNCTION AND SYMMETRIC DIFFERENCE OF TWO GRAPHS

2021 ◽  
Vol 10 (4) ◽  
pp. 2045-2052
Author(s):  
S. Menaka ◽  
R.S. Manikandan ◽  
R. Muruganandam
Keyword(s):  
Wiener Index ◽  
Symmetric Difference

scholarly journals Separability of the L1-space of a vector measure

1992 ◽  
Vol 34 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Werner J. Ricker
Keyword(s):  
Banach Space ◽  
Metric Space ◽  
Classical Result ◽  
Vector Measure ◽  
Symmetric Difference ◽  
Outer Measure ◽  
Additive Measure ◽  
Image Position

Let Σ be a σ-algebra of subsets of some set Ω and let μ:Σ→[0,∞] be a σ-additive measure. If Σ(μ) denotes the set of all elements of Σ with finite μ-measure (where sets equal μ-a.e. are identified in the usual way), then a metric d can be defined in Σ(μ) by the formulahere E ΔF = (E\F) ∪ (F\E) denotes the symmetric difference of E and F. The measure μ is called separable whenever the metric space (Σ(μ), d) is separable. It is a classical result that μ is separable if and only if the Banach space L1(μ), is separable [8, p.137]. To exhibit non-separable measures is not a problem; see [8, p. 70], for example. If Σ happens to be the σ-algebra of μ-measurable sets constructed (via outer-measure μ*) by extending μ defined originally on merely a semi-ring of sets Γ ⊆ Σ, then it is also classical that the countability of Γ guarantees the separability of μ and hence, also of L1(μ), [8, p. 69].

scholarly journals Specific Types of Pythagorean Fuzzy Graphs and Application to Decision-Making

2018 ◽  
Vol 23 (3) ◽  
pp. 42 ◽  
Author(s):  
Muhammad Akram ◽  
Amna Habib ◽  
Farwa Ilyas ◽  
Jawaria Dar
Keyword(s):  
Decision Making ◽  
Research Study ◽  
Symmetric Difference ◽  
Intuitionistic Fuzzy ◽  
Research Article ◽  
Fuzzy Graphs ◽  
Intuitionistic Fuzzy Graphs

The purpose of this research study is to present some new operations, including rejection, symmetric difference, residue product, and maximal product of Pythagorean fuzzy graphs (PFGs), and to explore some of their properties. This research article introduces certain notions, including intuitionistic fuzzy graphs of 3-type (IFGs3T), intuitionistic fuzzy graphs of 4-type (IFGs4T), and intuitionistic fuzzy graphs of n-type (IFGsnT), and proves that every IFG(n−1)T is an IFGnT (for n ≥ 2). Moreover, this study discusses the application of Pythagorean fuzzy graphs in decision making.

Minimal DFA for Symmetric Difference NFA

2012 ◽  
pp. 307-318 ◽  
Author(s):  
Brink van der Merwe ◽  
Hellis Tamm ◽  
Lynette van Zijl
Keyword(s):  
Symmetric Difference

scholarly journals Equations of quantum theory in the space of randomly joint quantum events

2019 ◽  
Vol 222 ◽  
pp. 03005
Author(s):  
Alexander Biryukov
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Effects ◽  
Symmetric Difference ◽  
System Transition ◽  
Additional Axiom ◽  
Random Events ◽  
Kolmogorov Axioms

The dynamics of the system in the space of random joint events is considered. The symmetric difference of events is introduced in space based on the Kolmogorov axioms. To describe quantum effects in the dynamics of the system, an additional axiom is introduced for random joint events: “the symmetric sum of random events.” In the generated space of random joint events, an equation is constructed for the probability of a system transition between two events. It is shown that for pairwise joint events it is equivalent to the equation of quantum mechanics.

Autometrization and the Symmetric Difference

1953 ◽  
Vol 5 ◽  
pp. 324-331 ◽  
Author(s):  
J. G. Elliott
Keyword(s):  
Boolean Algebra ◽  
Distance Function ◽  
Symmetric Difference ◽  
Group Operation ◽  
Metric Distance

The fact that the symmetric difference is a group operation in a Boolean algebra is, of course, well known. Not so well known is the fact observed by Ellis [3] that it possesses some of the desirable properties of a metric distance function. Specifically, if * denotes this operation, it is easy to verify that

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