Schubert’s Large-Scale Sentences

In this article, I share findings from analysis of first-movement sonata forms composed by Franz Schubert from 1810 to 1828. This work builds on prior studies of nineteenth-century sentences (e.g., ".fn_cite($baileyshea_2002).", ".fn_cite($bivens_2018).", ".fn_cite($broman_2007).", ".fn_cite($vandemoortele_2011).", and ".fn_cite($krebs_2013)."), offering an in-depth investigation of Schubert’s use of expanded sentence forms. I theorize the typical qualities of Schubert’s large-scale sentences and highlight a particularly common type, in which the large-scale continuation phrase begins as a third statement of the large-scale basic idea (i.e., a dissolving third statement). I present four examples of this formal type as representative, drawn from the C Major Symphony (D. 944/i), the C Minor Piano Sonata (D. 958/i), the C Major String Quintet (D. 956/i), and the D Minor String Quartet (D. 810/i). My analytical examples invite the reader to contemplate the negotiation of surface-level paratactic repetitions with deeper hypotactic structures. These large structures invite new modes of listening; exemplify the nineteenth-century shift away from the relative brevity of Classical precursors in favor of expanded forms; and problematize facile distinctions between inter- and intrathematic functions. This formal type would eventually flourish over the course of the nineteenth century, underpinning many composers’ strategies for formal expansion.

Logarithmic expansion of field theories: higher orders and resummations

A formal expansion for the Green’s functions of a quantum field theory in a parameter $$\delta $$ δ that encodes the “distance” between the interacting and the corresponding free theory was introduced in the late 1980s (and recently reconsidered in connection with non-hermitian theories), and the first order in $$\delta $$ δ was calculated. In this paper we study the $${\mathcal {O}}(\delta ^2)$$ O ( δ 2 ) systematically, and also push the analysis to higher orders. We find that at each finite order in $$\delta $$ δ the theory is non-interacting: sensible physical results are obtained only resorting to resummations. We then perform the resummation of UV leading and subleading diagrams, getting the $${\mathcal {O}}(g)$$ O ( g ) and $${\mathcal {O}}(g^2)$$ O ( g 2 ) weak-coupling results. In this manner we establish a bridge between the two expansions, provide a powerful and unique test of the logarithmic expansion, and pave the way for further studies.

Nonlinear fourth order Taylor expansion of lattice Boltzmann schemes

We propose a formal expansion of multiple relaxation times lattice Boltzmann schemes in terms of a single infinitesimal numerical variable. The result is a system of partial differential equations for the conserved moments of the lattice Boltzmann scheme. The expansion is presented in the nonlinear case up to fourth order accuracy. The asymptotic corrections of the nonconserved moments are developed in terms of equilibrium values and partial differentials of the conserved moments. Both expansions are coupled and conduct to explicit compact formulas. The new algebraic expressions are validated with previous results obtained with this framework. The example of isothermal D2Q9 lattice Boltzmann scheme illustrates the theoretical framework.

Expansion and Conflict at Oil Palm Plantations: A Case in Terantang Manuk Village, Pelalawan District, Riau

The massive expansion of oil palm plantations has social, economic and environmental impacts. One of the social impacts caused by the expansion of palm oil plantations is social conflict, so the purpose of this research is to identify and analyze the relationship between expansion and conflict in oil palm plantations in Terantang Manuk Village, Pelalawan-Riau. Palm oil plantation expansion is one of the factors for the emergence of social conflicts in rural areas. This research was conducted using a qualitative approach. Primary data were collected through in-depth interviews with the determination of the informants using purposive sampling technique. There were 16 informants who were interviewed, consisting of the village head, hamlet head, customary chairperson (ninik mamak), community leaders, chairperson of Cooperative Terantang Jaya Mandiri (TJM), leader of youth organization, and leader of college student organization. Secondary data quoted from archives of public correspondence, court decisions, and information from the mass media. The results of this study indicate that there are two types of expansion, namely informal expansion and formal expansion. Informal expansion only causes land conflicts, while formal expansion causes more diverse conflicts, namely land conflicts and conflicts due to oil palm plantation activities.

PROTECTED AREAS UNDER THE CONDITIONS OF MEGAPOLIS: DIGRESSION AND RECOVERY WAYS (ON THE EXAMPLE OF KYIV)

The purpose of the study is to identify the main causes of the protected ecosystems digression within the nature reserve fund (NRF) territories of Kyiv city and to substantiate measures to restore their conservation status. Through the analysis of mapping materials and regulations, using the QGIS software the map of the NRF objects distribution in Kyiv has been constructed. The area of these sites is also calculated and the degree of preservation in each administrative district of the city is determined. Each year, the Kyiv City Council declaratively extends the NRF area, but most of urban protected areas (UPA) do not accomplish their tasks and gradually lose the natural value previously created to preserve them. Due to the lack of funding and mismanagement, new ecological conflicts are emerging within these institutions and, as a result, degrading natural ecosystems. For example, the only urban National Natural Park (NNP) in Ukraine “Holosiyivskyi” since its inception in 1994 still has no official boundaries. Holosiyivskyi forest, the central part of the NNP, surrounded by residential buildings and highways from all sides, has the smallest area of reserved zone among the other Park massifs. Another illustrative example is the Lysa Hora Regional Landscape Park (RLP), where residential development comes close to its area. The RLP protected regime is disrupted along its existence and is only a declaration. Therefore, erosion processes are activated, red-book species die, nature use conflicts are widespread, ecosystem values are degraded. The study justifies the inefficiency of the NRF area further formal expansion in the Kyiv city. UPA activities largely do not meet the functions and criteria set by law. To improve the management of NRF institutions, it is proposed to change their functional zoning procedure and to transfer zoning on a landscape basis. In order to reduce the risk of illegal development near the UPA boundaries, it is necessary to develop land management projects for NRF institutions, to define their boundaries and to strengthen control over the implementation of Ukrainian environmental legislation. Creating buffer zones around the UPA protecting them from the adverse effects of urban infrastructure can prevent the chaotic development and further degradation of the ecosystems. The scientific novelty of the study is in identifying the causes of the digression of Kyiv’s protected areas and substantiating measures to overcome them. The spatial distribution of NRF institutions was determined and their structural and functional organization analyzed in order to achieve the purpose of the study.

The Role of Customary Land Ownership in Land-Use Conversion in the Peri-urban of Bukittinggi, Indonesia

Taluak is located in the peri-urban area of the city of Bukittinggi, in Agam Regency, West Sumatra, Indonesia. Bukittinggi is rapidly expanding into this peri-urban area. Due to a lack of sound land-use regulations, the growing population and increasing development are encroaching into the peri-urban area. In 1999, the administrative area of Bukittinggi was formally expanded to include some of the surrounding land that had previously been part of Agam Regency. However, although the physical development of the city has encroached into parts of Agam Regency, including Taluak, the communities of the village refused to be administratively included in Bukittinggi. One of their reasons for this refusal is a belief that such urbanization will harm the culture and traditions of the village. This article aims to explain how the communities of Taluak have resisted the formal expansion of Bukittinggi to include them in order to maintain their culture and traditions of land management and to estimate how long such resistance can survive. The article also explains how the process of land conversion in Taluak is carried out, particularly the conversion from rural use into urban use, which creates rurban (rural-urban) areas.

Enumeration of maps

This article discusses the relationship between random matrices and maps, i.e. graphs drawn on surfaces, with particular emphasis on the one-matrix model and how it can be used to solve a map enumeration problem. It first provides an overview of maps and related objects, recalling the basic definitions related to graphs and defining maps as graphs embedded into surfaces before considering a coding of maps by pairs of permutations. It then examines the connection between matrix integrals and maps, focusing on the Hermitian one-matrix model with a polynomial potential and how the formal expansion of its free energy around a Gaussian point (quadratic potential) can be represented by diagrams identifiable with maps. The article also illustrates how the solution of the map enumeration problem can be deduced by means of random matrix theory (RMT). Finally, it explains how the matrix model result can be translated into a bijective proof.

THE COUPLED-CLUSTER APPROACH TO QUANTUM MANY-BODY PROBLEM IN A THREE-HILBERT-SPACE REINTERPRETATION

The quantum many-body bound-state problem in its computationally successful coupled cluster method (CCM) representation is reconsidered. In conventional practice one factorizes the groundstate wave functions |Ψ) = e^S |Φ) which live in the “physical” Hilbert space H^(P) using an elementary ansatz for |Φi plus a formal expansion of S in an operator basis of multi-configurational creation operators C⁺. In our paper a reinterpretation of the method is proposed. Using parallels between the CCM and the so called quasi-Hermitian, <em>alias</em> three-Hilbert-space (THS), quantum mechanics, the CCM transition from the known microscopic Hamiltonian (denoted by usual symbol <em>H</em>), which is self-adjoint in <em>H^(P)</em>, to its effective lower-case isospectral avatar <em>h = e^−SHe^S</em>, is assigned a THS interpretation. In the opposite direction, a THS-prescribed, non-CCM, innovative reinstallation of Hermiticity is shown to be possible for the CCM effective Hamiltonian <em>h</em>, which only appears manifestly non-Hermitian in its own (“friendly”) Hilbert space <em>H^(F)</em>. This goal is achieved via an ad hoc amendment of the inner product in <em>H^(F)</em>, thereby yielding the third (“standard”) Hilbert space <em>H^(S)</em>. Due to the resulting exact unitary equivalence between the first and third spaces, <em>H^(F)</em> ∼ <em>H^(S)</em>, the indistinguishability of predictions calculated in these alternative physical frameworks is guaranteed.