The Strong Property (B) for $$L_p$$ Spaces

Given a purely non-atomic, finite measure space $$(\Omega ,\Sigma ,\nu )$$ ( Ω , Σ , ν ) , it is proved that for every closed, infinite-dimensional subspace V of $$L_p(\nu )$$ L p ( ν ) ($$1\le p<\infty $$ 1 ≤ p < ∞ ) there exists a decomposition $$L_p(\nu )=X_1\oplus X_2$$ L p ( ν ) = X 1 ⊕ X 2 , such that both subspaces $$X_1$$ X 1 and $$X_2$$ X 2 are isomorphic to $$L_p(\nu )$$ L p ( ν ) and both $$V\cap X_1$$ V ∩ X 1 and $$V\cap X_2$$ V ∩ X 2 are infinite-dimensional. Some consequences concerning dense, non-closed range operators on $$L_1$$ L 1 are derived.

The International Role of the U.S. Dollar

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.

Constant-Length Labeling Schemes for Deterministic 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

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.

On partially Schur-constant models and their associated copulas

Schur-constant vectors are used to model duration phenomena in various areas of economics and statistics. They form a particular class of exchangeable vectors and, as such, rely on a strong property of symmetry. To broaden the field of applications, partially Schur-constant vectors are introduced which correspond to partially exchangeable vectors. First, their copulas of survival, said to be partially Archimedean, are explicitly obtained and analyzed. Next, much attention is devoted to the construction of different partially Schur-constant models with two groups of exchangeable variables. Finally, partial Schur-constancy is briefly extended to the modeling of nested and multi-level dependencies.

Historical origins of land rights insecurity and implications for conflict in Thailand

This article explores the historical origins of land rights insecurity and its implications for landlessness, poverty, and contemporary conflict in Thailand. The Siamese (now Thai) government adopted the Torrens system of land administration in 1901 as part of a larger strategy to curb colonial territorial expansion in Southeast Asia. Although the Torrens system is generally associated with strong property rights, its incomplete and uneven adoption led to widespread and long-running land rights insecurity and landlessness. This article presents two case studies that demonstrate these consequences. First, the expropriation of land through the exploitation of ambiguous land rights and the implementation of new land laws. Second, the long-run associations between land rights insecurity, low levels of productive investments in agriculture, and poverty. Consequent landlessness and poverty in agricultural communities have, in turn, led to recent protests and violence in Thailand.

Protecting Homes and Other Types of Property

This chapter questions the tendency of property law to bestow more generous protection against dispossession due to debts or other losses to residential property than to personal or commercial property or leasehold interests (i.e., renters). Contrary to this pattern in property law, the empirical psychology research on homes suggests only moderate psychological importance to maintaining ownership of one’s particular home, and substantial attachments and psychological interests in personal and commercial property. From the perspective of psychological loss, the strong property protection afforded to homes under tenancy by the entirety and homestead exemptions may be outsized. Conversely, the more limited protection of personal property and compensation for its loss under laws such as bankruptcy exemptions and bailment may be inadequate.

On proper strong Property (𝒜) for rings and modules

The main purpose of this paper is to introduce and investigate a new class of rings lying properly between the class of [Formula: see text]-rings and the class of [Formula: see text]-rings. The new class of rings, termed the class of [Formula: see text]-rings, turns out to share common characteristics with both [Formula: see text]-rings and [Formula: see text]-rings. Numerous properties and characterizations of this class are given as well as the module-theoretic version of [Formula: see text]-rings is introduced and studied.

When is the idealization R⋉M an 𝒜-ring?

We present an answer to a problem raised by Anderson and Chun in [D. D. Anderson and S. Chun, Annihilator conditions on modules over commutative rings, J. Algebra Appl. 16(7) (2017) 1750143] on characterizing when the idealization [Formula: see text] of a ring [Formula: see text] on an [Formula: see text]-module [Formula: see text] is an [Formula: see text]-ring (respectively, an [Formula: see text]-ring) in terms of module-theoretic properties of [Formula: see text] and [Formula: see text]. Also, we are concerned with an open question asked by these two authors which reads the following: What modules over a given ring [Formula: see text] are homomorphic images of modules satisfying the strong Property [Formula: see text]? (see, Question 4.4(1) in the above mentioned paper). This paper highly contributes to answer such a question.