Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor

The integrability of an m-component system of hydrodynamic type, u_t=V(u)u_x, by the generalized hodograph method requires the diagonalizability of the mxm matrix V(u). This condition is known to be equivalent to the vanishing of the corresponding Haantjes tensor. We generalize this approach to hydrodynamic chains -- infinite-component systems of hydrodynamic type for which the infinite matrix V(u) is `sufficiently sparse'. For such systems the Haantjes tensor is well-defined, and the calculation of its components involves finite summations only. We illustrate our approach by classifying broad classes of conservative and Hamiltonian hydrodynamic chains with the zero Haantjes tensor. We prove that the vanishing of the Haantjes tensor is a necessary condition for a hydrodynamic chain to possess an infinity of semi-Hamiltonian hydrodynamic reductions, thus providing an easy-to-verify necessary condition for the integrability.Comment: 36 pages, the classification results and proofs are refined. A section on generating functions is adde

The Rise of State-Specific Attempts to Decipher the Sufficiency-of-a-Debtor-Name Standard Under Revised Article 9 and the End of Uniformity in Secured Transactions

This is the published version

Extreme Policy Makeover: Re-Evaluating Current U.S.-Vietnam Relations under the International Religious Freedom Act

Following the signing of the Paris Peace Accord in 1973, the relationship between the United States and Vietnam remained essentially frozen. In 2000, the signing of the United States-Vietnam Bilateral Trade Agreement was an epic step in the normalization of relations. In addition, the BTA was hailed as a means of effectuating positive change in the area of Vietnam\u27s human rights. Unfortunately, the state of religious freedom in Vietnam has deteriorated while economic ties with the United States have strengthened. Despite Vietnam\u27s purported respect for religious freedom, violations continue. Vietnam restricts the practice of religion, detains religious leaders, and tolerates forced renunciations of faith by local officials. These acts violate the International Covenant on Civil and Political Rights, to which Vietnam has acceded. Vietnam\u27s violations of the right to religious freedom have also drawn the concern of the international community. Specifically, the United States has called for improvements in Vietnam\u27s religious rights record, utilizing diplomatic mean coupled with continued engagement in the hopes that Vietnam will voluntarily enact changes. However, this approach has failed to yield concrete progress. In 2004, the U.S. Department of State designated Vietnam a Country of Particular Concern as provided in the International Religious Freedom Act. Because the IRFA mandates affirmative action against violators of religious freedom, the United States must abandon constructive engagement in Vietnam. Instead, the IRFA provides the framework for opposing violations under the responsible engagement doctrine. In doing so, the United States may employ economic pressure to narrowly target violators, while allowing the liberalizing effect of engagement to continue where it does not sustain violations. By fully implementing the IRFA in accordance with the tenets of responsible engagement, the United States would actively oppose violations rather than engaging Vietnam with the hope that improvements will occur. Moreover, this extreme makeover of current policy would balance the dual interests of improved religious freedom and bilateral relations

The role of the material fracture properties in the size-effect law of concrete structures

The size effect of the nominal stress at failure in concrete structures is dealt within general. An existence of a rather large fracture process zone in front of crack tip is proved to be the main reason leading to the size effect of the nominal strength. On the basis of the new general size-effect law and numerical results of fracture propagation, a particularly proposed size effect law for beams in bending is developed, in which the role of each material fracture characteristic, especially the shape of the stress - crack opening curve, is elaborated clearly

Blockchain Stock Ledgers

American corporate law contains a seemingly innocuous mandate. Corporations must maintain appropriate books and records, including a stock ledger with the corporation\u27s shareholders and stock ownership. The importance of accurate stock ownership records is obvious. Corporations must know who owns each of its outstanding shares at any point in time. Among other things, this allows corporations to determine who receives dividends and who is entitled to vote. In theory, keeping accurate records of stock ownership should be a simple matter. But despite diligent efforts, serious share discrepancies plague corporations, and reconciliation is often functionally impossible. Doing so may require the examination of records from millions of trades, including records from hundreds of participant brokers and custodial banks (not to mention records from their individual clients). So, when disputes arise, there is frequently no easy answer. This Article charts the use of blockchain technology as a potential solution to the systemic issues hindering efforts to maintain accurate records of stock transactions. In doing so, this Article accomplishes three goals. First, it establishes that federal efforts to resolve the paperwork crisis of the 1970\u27s created a concomitant problem the lack of reliable records of stock ownership, which now threatens the exercise of shareholder rights. Second, it demonstrates that practical constraints, not legal barriers, stand as the most significant impediment to the application of blockchain technology to corporate recordkeeping and global capital markets. Third, it argues that despite reasons for skepticism, states should proactively amend corporate codes to authorize the use of blockchain technology because it enables corporate choice and facilitates efforts by private actors to assess the viability of innovative solutions. This Article concludes by drawing transferable lessons to improve law and policy as new applications of blockchain technology continue to emerge

Picard group of hypersurfaces in toric 3-folds

We show that the usual sufficient criterion for a generic hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to hypersurfaces in complete simplicial toric varieties. This sufficient condition is always satisfied by generic K3 surfaces embedded in Fano toric 3-folds.Comment: 14 pages. v2: some typos corrected. v3: Slightly changed title. Final version to appear in Int. J. Math., incorporates many (mainly expository) changes suggested by the refere

String order and hidden topological symmetry in the SO(2n+1) symmetric matrix product states

We have introduced a class of exactly soluble Hamiltonian with either SO(2n+1) or SU(2) symmetry, whose ground states are the SO(2n+1) symmetric matrix product states. The hidden topological order in these states can be fully identified and characterized by a set of nonlocal string order parameters. The Hamiltonian possesses a hidden $(Z_{2}\times Z_{2})^{n}$ topological symmetry. The breaking of this hidden symmetry leads to $4^{n}$ degenerate ground states with disentangled edge states in an open chain system. Such matrix product states can be regarded as cluster states, applicable to measurement-based quantum computation.Comment: 5 pages, 1 figur

Inactivation of mammalian Ero 1α is catalysed by specific protein disulfide isomerases

Disulfide formation within the endoplasmic reticulum is a complex process requiring a disulfide exchange protein such as protein disulfide isomerase and a mechanism to form disulfides de novo. In mammalian cells, the major pathway for de novo disulfide formation involves the enzyme Ero1α which couples oxidation of thiols to the reduction of molecular oxygen to form hydrogen peroxide. Ero1α activity is tightly regulated by a mechanism that requires the formation of regulatory disulfides. These regulatory disulfides are reduced to activate and reform to inactive the enzyme. To investigate the mechanism of inactivation we analysed regulatory disulfide formation in the presence of various oxidants under controlled oxygen concentration. Neither molecular oxygen, nor hydrogen peroxide was able to oxidise Ero1α efficiently to form the correct regulatory disulfides. However, specific members of the PDI family such as PDI or ERp46 were able to catalyse this process. Further studies showed that both active sites of PDI contribute to the formation of regulatory disulfides in Ero1α and that the PDI substrate binding domain is crucial to allow electron transfer between the two enzymes. These results demonstrate a simple feedback mechanism of regulation of mammalian Ero1α involving its primary substrate

Cyclic cocycles on twisted convolution algebras

We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted convolution algebra and twisted cohomology groups which is similar to a construction of Mathai and Stevenson. When the groupoid is not proper, we cannot construct an invariant connection on the gerbe; therefore to study this algebra, we instead develop simplicial techniques to construct a simplicial curvature 3-form representing the class of the gerbe. Then by using a JLO formula we define a morphism from a simplicial complex twisted by this simplicial curvature 3-form to the mixed bicomplex computing the periodic cyclic cohomology of the twisted convolution algebras. The results in this article were originally published in the author's Ph.D. thesis.Comment: 39 page