On a strong property of the weak subalgebra lattice

1998 ◽  
Vol 40 (4) ◽  
pp. 477 ◽  
Author(s):  
K. Pióro
Keyword(s):  
Subalgebra Lattice ◽  
Strong Property

A STRONG PROPERTY OF THE WEAK SUBALGEBRA LATTICE FOR LOCALLY FINITE ALGEBRAS OF FINITE TYPE

2013 ◽  
Vol 23 (01) ◽  
pp. 1-35
Author(s):  
KONRAD PIÓRO
Keyword(s):  
Finite Type ◽  
Locally Finite ◽  
Finite Algebras ◽  
Edge Disjoint ◽  
Subalgebra Lattice ◽  
Strong Property ◽  
Directed Hypergraphs ◽  
Algebraic Result ◽  
Directed Hypergraph

The aim of this paper is to show that the weak subalgebra lattice uniquely determines the subalgebra lattice for locally finite algebras of a fixed finite type. However, this algebraic result turns out to be a very particular case of the following hypergraph result (which is interesting itself): A total directed hypergraph D of finite type is uniquely determined, in the class of all the directed hypergraphs of this type, by its skeleton up to the orientation of some pairwise edge-disjoint directed hypercycles and hyperpaths. The skeleton of D is a hypergraph obtained from D by omitting the orientation of all edges.

scholarly journals Unconditional C-strong property of Faber–Schauder system

2009 ◽  
Vol 352 (2) ◽  
pp. 718-723 ◽  
Author(s):  
M.G. Grigoryan ◽  
A.A. Sargsyan
Keyword(s):  
Strong Property

scholarly journals Constant-Length Labeling Schemes for Deterministic Radio Broadcast

2021 ◽  
Vol 8 (3) ◽  
pp. 1-17
Author(s):  
Faith Ellen ◽  
Barun Gorain ◽  
Avery Miller ◽  
Andrzej Pelc
Keyword(s):  
Collision Detection ◽  
Background Noise ◽  
A Priori ◽  
Deterministic Algorithm ◽  
Radio Networks ◽  
Positive Answer ◽  
Radio Network ◽  
Constant Length ◽  
Strong Property ◽  
Radio Broadcast

Broadcast is one of the fundamental network communication primitives. One node of a network, called the s ource, has a message that has to be learned by all other nodes. We consider broadcast in radio networks, modeled as simple undirected connected graphs with a distinguished source. Nodes communicate in synchronous rounds. In each round, a node can either transmit a message to all its neighbours, or stay silent and listen. At the receiving end, a node v hears a message from a neighbour w in a given round if v listens in this round and if w is its only neighbour that transmits in this round. If more than one neighbour of a node v transmits in a given round, we say that a c ollision occurs at v . We do not assume collision detection: in case of a collision, node v does not hear anything (except the background noise that it also hears when no neighbour transmits). We are interested in the feasibility of deterministic broadcast in radio networks. If nodes of the network do not have any labels, deterministic broadcast is impossible even in the four-cycle. On the other hand, if all nodes have distinct labels, then broadcast can be carried out, e.g., in a round-robin fashion, and hence O (log n )-bit labels are sufficient for this task in n -node networks. In fact, O (log Δ)-bit labels, where Δ is the maximum degree, are enough to broadcast successfully. Hence, it is natural to ask if very short labels are sufficient for broadcast. Our main result is a positive answer to this question. We show that every radio network can be labeled using 2 bits in such a way that broadcast can be accomplished by some universal deterministic algorithm that does not know the network topology nor any bound on its size. Moreover, at the expense of an extra bit in the labels, we can get the following additional strong property of our algorithm: there exists a common round in which all nodes know that broadcast has been completed. Finally, we show that 3-bit labels are also sufficient to solve both versions of broadcast in the case where it is not known a priori which node is the source.

Everlasting security of quantum key distribution with 1K-DWCDM and quadratic hash

2021 ◽  
Vol 21 (3&4) ◽  
pp. 0181-0202
Author(s):  
Khodakhast Bibak ◽  
Robert Ritchie ◽  
Behrouz Zolfaghari
Keyword(s):  
Hash Function ◽  
Quantum Key Distribution ◽  
Key Distribution ◽  
Privacy Amplification ◽  
Universal Hashing ◽  
Wide Range ◽  
Strong Property ◽  
Everlasting Security ◽  
Universal Hash Function ◽  
General Method

Quantum key distribution (QKD) offers a very strong property called everlasting security, which says if authentication is unbroken during the execution of QKD, the generated key remains information-theoretically secure indefinitely. For this purpose, we propose the use of certain universal hashing based MACs for use in QKD, which are fast, very efficient with key material, and are shown to be highly secure. Universal hash functions are ubiquitous in computer science with many applications ranging from quantum key distribution and information security to data structures and parallel computing. In QKD, they are used at least for authentication, error correction, and privacy amplification. Using results from Cohen [Duke Math. J., 1954], we also construct some new families of $\varepsilon$-almost-$\Delta$-universal hash function families which have much better collision bounds than the well-known Polynomial Hash. Then we propose a general method for converting any such family to an $\varepsilon$-almost-strongly universal hash function family, which makes them useful in a wide range of applications, including authentication in QKD.

The International Role of the U.S. Dollar

FEDS Notes ◽  
2021 ◽  
Vol 2021 (2998) ◽  
Author(s):  
Carol Bertaut ◽  
◽  
Bastian von Beschwitz ◽  
Stephanie Curcuru ◽  
◽  
...  
Keyword(s):  
Financial Markets ◽  
Rule Of Law ◽  
Capital Flows ◽  
Global Economy ◽  
The Rule Of Law ◽  
Strong Property ◽  
International Role ◽  
Openness To Trade ◽  
The U.S

For most of the last century, the preeminent role of the U.S. dollar in the global economy has been supported by the size and strength of the U.S. economy, its stability and openness to trade and capital flows, and strong property rights and the rule of law. As a result, the depth and liquidity of U.S. financial markets is unmatched, and there is a large supply of extremely safe dollar-denominated assets.

The subalgebra lattice of a Heyting algebra

1987 ◽  
Vol 37 (1) ◽  
pp. 34-41 ◽  
Author(s):  
L. Vrancken-Mawet ◽  
Georges Hansoul
Keyword(s):  
Heyting Algebra ◽  
Subalgebra Lattice

Diagnosability of Bubble-Sort Star Graphs with Missing Edges

2019 ◽  
Vol 19 (02) ◽  
pp. 1950002 ◽  
Author(s):  
SHIYING WANG ◽  
YINGYING WANG
Keyword(s):  
Multiprocessor System ◽  
Star Graph ◽  
Star Graphs ◽  
Comparison Model ◽  
Model Following ◽  
Strong Property

The diagnosability of a multiprocessor system plays an important role. The bubble-sort star graph BSn has many good properties. In this paper, we study the diagnosis on BSn under the comparison model. Following the concept of the local diagnosability, the strong local diagnosability property is discussed. This property describes the equivalence of the local diagnosability of a node and its degree. We prove that BSn (n ≥ 5) has this property, and it keeps this strong property even if there exist (2n − 5) missing edges in it, and the result is optimal with respect to the number of missing edges.

scholarly journals ON SEMI-MODULAR SUBALGEBRAS OF LIE ALGEBRAS OVER FIELDS OF ARBITRARY CHARACTERISTIC

2008 ◽  
Vol 01 (02) ◽  
pp. 283-294 ◽  
Author(s):  
DAVID A. TOWERS
Keyword(s):  
Lie Algebras ◽  
Extensive Study ◽  
Two Dimensional ◽  
Perfect Field ◽  
Characteristic P ◽  
Subalgebra Lattice ◽  
Closed Fields ◽  
The One ◽  
Algebraically Closed Fields ◽  
Number Of Authors

This paper is a further contribution to the extensive study by a number of authors of the subalgebra lattice of a Lie algebra. It is shown that, in certain circumstances, including for all solvable algebras, for all Lie algebras over algebraically closed fields of characteristic p > 0 that have absolute toral rank ≤ 1 or are restricted, and for all Lie algebras having the one-and-a-half generation property, the conditions of modularity and semi-modularity are equivalent, but that the same is not true for all Lie algebras over a perfect field of characteristic three. Semi-modular subalgebras of dimensions one and two are characterised over (perfect, in the case of two-dimensional subalgebras) fields of characteristic different from 2, 3.

scholarly journals Lower semimodular Lie algebras

1999 ◽  
Vol 42 (3) ◽  
pp. 521-540 ◽  
Author(s):  
V. R. Varea
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Maximal Subalgebras ◽  
Modular Element ◽  
Subalgebra Lattice ◽  
The Relationship

This paper is concerned with the relationship between the properties of the subalgebra lattice ℒ(L) of a Lie algebra L and the structure of L. If the lattice ℒ(L) is lower semimodular, then the Lie algebra L is said to be lower semimodular. If a subalgebra S of L is a modular element in the lattice ℒ(L), then S is called a modular subalgebra of L. The easiest condition to ensure that L is lower semimodular is that dim A/B = 1 whenever B < A ≤ L and B is maximal in A (Lie algebras satisfying this condition are called sχ-algebras). Our aim is to characterize lower semimodular Lie algebras and sχ-algebras, over any field of characteristic greater than three. Also, we obtain results about the influence of two solvable modularmaximal subalgebras on the structure of the Lie algebra and some results on the structure of Lie algebras all of whose maximal subalgebras are modular.

Sign in / Sign up

Export Citation Format

Share Document