The ABC of Physics

Why quantum? Why spacetime? We find that the key idea underlying both is uncertainty. In a world lacking probes of unlimited delicacy, our knowledge of quantities is necessarily accompanied by uncertainty. Consequently, physics requires a calculus of number pairs and not only scalars for quantity alone. Basic symmetries of shuffling and sequencing dictate that pairs obey ordinary component-wise addition, but they can have three different multiplication rules. We call those rules A, B and C. “A” shows that pairs behave as complex numbers, which is why quantum theory is complex. However, consistency with the ordinary scalar rules of probability shows that the fundamental object is not a particle on its Hilbert sphere but a stream represented by a Gaussian distribution. “B” is then applied to pairs of complex numbers (qubits) and produces the Pauli matrices for which its operation defines the space of four vectors. “C” then allows integration of what can then be recognised as energy-momentum into time and space. The picture is entirely consistent. Spacetime is a construct of quantum and not a container for it.

Hamiltonian structures for integrable hierarchies of Lagrangian PDEs

Many integrable hierarchies of differential equations allow a variational description, called a Lagrangian multiform or a pluri-Lagrangian structure. The fundamental object in this theory is not a Lagrange function but a differential $d$-form that is integrated over arbitrary $d$-dimensional submanifolds. All such action integrals must be stationary for a field to be a solution to the pluri-Lagrangian problem. In this paper we present a procedure to obtain Hamiltonian structures from the pluri-Lagrangian formulation of an integrable hierarchy of PDEs. As a prelude, we review a similar procedure for integrable ODEs. We show that exterior derivative of the Lagrangian $d$-form is closely related to the Poisson brackets between the corresponding Hamilton functions. In the ODE (Lagrangian 1-form) case we discuss as examples the Toda hierarchy and the Kepler problem. As examples for the PDE (Lagrangian 2-form) case we present the potential and Schwarzian Korteweg-de Vries hierarchies, as well as the Boussinesq hierarchy.

Aportaciones a la historia del género ambiguo en español: a propósito del sustantivo deverbal tizne

The New Grammar of the Spanish Language (2009) defines ambiguous nouns in terms of gender as those that refer to the same inanimate entity, both male and female, «but do not usually designate sexed beings». Some can be analyzed as late developments, after the restructuring of gender that followed the loss of neutral and casual flexion, together with verbs roots that show similar vacillations to those originated after the evolutionary processes that emerged in the transition from Latin into Romance languages. Among them we find the case of the word tizne, whose variations throughout the history of the Spanish language will be the fundamental object of the present study.

The Operational Choi–Jamiołkowski Isomorphism

In this article, I use an operational formulation of the Choi–Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be understood as a means of drawing conclusions about the intratheoretic causal structure of quantum mechanics which are independent of any specific ontological picture. I then give an operational formulation of the Choi–Jamiołkowski isomorphism and show that, in an operational theory which exhibits this isomorphism, several features of the theory which are usually regarded as properties of the quantum state can be derived from constraints on non-local correlations. This demonstrates that there is no need to postulate states to be the bearers of these properties, since they can be understood as consequences of a fundamental equivalence between multipartite and temporal correlations.

TYPES OF TERRITORIAL COMMUNITIES IN WHICH A HUMAN – A MEMBER OF THE COMMUNITY FUNCTIONS

The article is devoted to the study of human participation as a member of the community in the existence and functioning of the territorial community. The article contains a description of the types of territorial communities, as well as their general features. The article defines the way a person functions as a member of the community in the territorial community. It is determined that the territorial communities of the primary level are those communities in which a person fully realizes his right to local self- government, including, first of all, the realization of their existential interests and other needs due to the implementation of human life cycle within the territorial community. , mainly in the ordinary implementation of statehood. It is noted that the activities of local councils and their executive bodies in the understanding of teleological guidelines are carried out on behalf of and in the interests of the respective territorial communities, so there is a clear methodological and procedural link that arises in the implementation of these rights and interests. This issue is quite relevant, because most local communities and their members focus and concretize their needs and interests through the formation of key issues of local importance, which is a fundamental object of the institution of local government and local government. It is determined that the possibilities of territorial communities to determine their own administrative structures are quite limited in Ukraine, they are quite exhaustively defined centrally – in the relevant Law of Ukraine "On Local Self-Government in Ukraine". In addition, the cities of Kyiv and Sevastopol have not yet established their own executive structures of local self-government, and their functions are entrusted to the relevant local state administrations. This significantly limits the implementation of the principle of organizational autonomy.

MODIFICACIÓN DEL REGLAMENTO GENERAL DE REGISTROS PÚBLICOS PARA ESTABLECER LA RESPONSABILIDAD CIVIL DE LOS REGISTRADORES PÚBLICOS

El objetivo general de la investigación fue elaborar una propuesta de modificación al Reglamento General de Registros Públicos para establecer la responsabilidad civil de los registradores públicos, lo que mejoraría la calificación de los asientos registrales. La responsabilidad civil por parte de los registradores públicos derivados de la mala calificación registral es una obligación a cargo de quien, actuando de manera antijurídica y culpable en sus actos causa daños y perjuicios a terceros, de subsanar e indemnizar el agravio efectuado Nuestro sistema registral es una institución pública garante de la seguridad jurídica registral, puesto que dicha institución tiene a su cargo y como objeto fundamental la inscripción, anotación y cancelación de los actos y contratos relativos al dominio y demás derechos reales sobre inmuebles y muebles identificables. Las distintas anomalías que presentan el Registro Público perjudican, en la mayoría de ocasiones, directamente a los usuarios, en virtud que la mayor parte de estos no cuentan con una asesoría jurídica adecuada que lo oriente sobre como el Registrador puede responder por los daños y perjuicios causados a sus personas y a su patrimonio. Este hecho deja a merced cualquier mala práctica o mal acto de función por parte del Registrador y Registradores auxiliares de dicho registro.Todo daño o perjuicio causado a un tercero por el Registrador hace nacer un derecho a reparación en la persona o en su patrimonio y un deber de reparación con carga al Estado. Abstract The general objective of the investigation was to elaborate a proposal of modification to the General Regulation of Public Registries to establish the civil responsibility of the public registrars, which would improve the qualification of the registry entries.The civil responsibility on the part of public registrars derived from the bad registry qualification is an obligation in charge of who, acting of unlawful and guilty way in its acts causes damages and damages to third parties, of correcting and indemnifying the offense made. Our registry system is a public institution guaranteeing the legal security of the registry, since said institution is in charge of and as a fundamental object the registration, annotation and cancellation of the acts and contracts related to the domain and other real rights over immovable property and furniture. The different anomalies presented by the Public Registry damage, in most cases, directly to users, because most of these do not have adequate legal advice to guide them on how the Registrar can respond for damages caused to their people and their heritage. This fact leaves to mercy any bad practice or bad act of function on the part of the Registrar and Auxiliary Registrars of said registry Any damage or injury caused to a third party by the Registrar gives rise to a right to compensation in the person or in his / her patrimony and a duty of reparation charged to the State. Keywords: Registrar, registry entries, bad rating, civil liability, public records regulations.

ON STABILITY OF PHYSICALLY REASONABLE SOLUTIONS TO THE TWO-DIMENSIONAL NAVIER–STOKES EQUATIONS

The flow past an obstacle is a fundamental object in fluid mechanics. In 1967 Finn and Smith proved the unique existence of stationary solutions, called the physically reasonable solutions, to the Navier–Stokes equations in a two-dimensional exterior domain modeling this type of flows when the Reynolds number is sufficiently small. The asymptotic behavior of their solution at spatial infinity has been studied in detail and well understood by now, while its stability has remained open due to the difficulty specific to the two-dimensionality. In this paper, we prove that the physically reasonable solutions constructed by Finn and Smith are asymptotically stable with respect to small and well-localized initial perturbations.