Inverse Problem Related to Boundary Shape Identification for a Hyperbolic Differential Equation

In this paper, we are interested in the inverse problem of the determination of the unknown part ∂ Ω , Γ 0 of the boundary of a uniformly Lipschitzian domain Ω included in ℝ N from the measurement of the normal derivative ∂ n v on suitable part Γ 0 of its boundary, where v is the solution of the wave equation ∂ t t v x , t − Δ v x , t + p x v x = 0 in Ω × 0 , T and given Dirichlet boundary data. We use shape optimization tools to retrieve the boundary part Γ of ∂ Ω . From necessary conditions, we estimate a Lagrange multiplier k Ω which appears by derivation with respect to the domain. By maximum principle theory for hyperbolic equations and under geometrical assumptions, we prove a uniqueness result of our inverse problem. The Lipschitz stability is established by increasing of the energy of the system. Some numerical simulations are made to illustrate the optimal shape.

Monitoring and Analysis of Stress Distribution of the Interaction between Rock and Backfill and the Influence of Geometric Features of the Backfill Boundary

Backfill mining methods are widely used in metal mines. The boundary part of the backfill has a direct effect on the local stability in mining engineering. The distribution of stress on the boundary part of the backfill and surrounding rock had their own features. To study the characteristics of stress distribution of backfill and surrounding rock on the boundary part, we conducted a field investigation, field monitoring, and numerical simulation. According to the underground monitoring, the overall characteristics of the boundary part of the backfill were that the accumulated horizontal stress was larger than the accumulated vertical stress on the deep sublevel and the accumulated horizontal stress was smaller on the shallow sublevel. On the contact zone (i.e., the boundary part), the stress of the surrounding rock was larger than the stress of the backfill. Combined with the numerical model analysis, we determined that the geometric features of the backfill boundary had an influence on the stress distribution of stress. The multistep boundary helped the integrity of the contact zone and local stability in deep mining.

Monitoring and Analysis of Stress and Deformation Features of Boundary Part of Backfill in Metal Mine

The backfill mining method is widely used in metal mines. A large and thick backfill body has formed in the No.2 zone of Jinchuan Nickel Mine, and its stability is critical for mining safety. In order to study the mechanical behavior of the boundary part of backfill, ground subsidence monitoring, underground filed monitoring of displacement, and stress and numerical simulation were conducted to analyze stress distribution and deformation of backfill. According to underground monitoring, the bed separated displacement has the consistent trend with ground subsidence in the mine area. Based underground stress monitoring, both horizontal and vertical stress of the internal part of backfill is less than the stress boundary part of the backfill. The characteristic of backfill boundary outline is a step-profile. Contact interaction between the surrounding rock and backfill led to complex stress distribution. According to stress monitoring of the boundary points in a numerical model, the multi-peak value of stress development is the major feature of the boundary part of backfill. The multi-peak stress behavior of the boundary part of backfill was influenced by mining depth. The boundary part of backfill deformation influenced the local stability of mining. This article provided a scientific basis for strength design and the support choice of a metal mine by the method of backfill mining.

The perception of prominence: a Rapid Prosody Transcription study with Estonian listeners

This study investigates the effect of different prosodic variables (e.g., pitch, syllable duration, presence of pitch accent and intonation boundary) and non-prosodic variables (e.g., type of verbal argument, presence of clause boundary, part-of-speech and number of syllables) on the perception of prominence in spontaneous Estonian. Following the methodology of Rapid Prosody Transcription, 396 randomly selected speech fragments from ten speakers were presented over the internet to 51 prosodically untrained listeners, whose task was to highlight the words they heard as prominent. The same dataset was annotated for intonational pitch accents and boundary tones by two experts. The results demonstrate that the strongest predictors of prominence perception are the pitch and duration of stressed syllables together with the presence of a pitch accent while the non-prosodic variables are somewhat weaker. The study corroborates earlier findings in that the perceptual salience in spoken language processing depends largely on the acoustic signal-based cues. Kokkuvõte. Nele Ots ja Eva Liina Asu: Prominentsuse taju eesti keeles: prosoodia kiirtranskribeerimise uurimus eesti keele kõnelejatega. Artikkel uurib eri prosoodiliste tunnuste (põhitoon, rõhulise silbi kestus, tooni aktsendi ja intonatsioonipiiri olemasolu) ning mitteprosoodiliste tunnuste (verbi argument, klausipiiri olemasolu, sõnaliik ja silpide arv) mõju prominentsuse tajule spontaanses eesti keeles. Lähtudes prosoodia kiirtranskriptsiooni (Rapid Prosody Transcription, RPT) metodoloogiast, esitati 396 juhuslikult valitud spontaanse kõne lõiku interneti teel 51-le prosoodia valdkonnas koolitamata kuulajale, kelle ülesandeks oli tekstis esile tõsta sõnad, mis kuuldusid neile rõhulisena. Kaks kõneprosoodia uurijat transkribeerisid samades kõne lõikudes tooniaktsendid ja intonatsioonipiirid. Tulemused näitavad, et prominentsuse taju tähtsaimad ennustajad on tooniaktsent, põhitoon ning silbi kestus. Mitteprosoodilised tunnused mõjutavad prominentsuse taju mõnevõrra vähem. Katse tulemused kinnitavad varasemate uurimuste järeldust, et tajutud prominentsus sõltub eelkõige akustilistest signaalipõhistest tunnustest. Märksõnad: prominentsus, taju, intonatsioon, tooniaktsent, sõnaliik, argumendistruktuur, prosoodia kiirtranskriptsioon (RPT), eesti keel

Lozenge Tilings of a Halved Hexagon with an Array of Triangles Removed from the Boundary, Part II

Proctor's work on staircase plane partitions yields an exact enumeration of lozenge tilings of a halved hexagon on the triangular lattice. Rohatgi later extended this tiling enumeration to a halved hexagon with a triangle cut off from the boundary. In his previous paper, the author proved a common generalization of Proctor's and Rohatgi's results by enumerating lozenge tilings of a halved hexagon in the case an array of an arbitrary number of triangles has been removed from a non-staircase side. In this paper we consider the other case when the array of triangles has been removed from the staircase side of the halved hexagon. Our result also implies an explicit formula for the number of tilings of a hexagon with an array of triangles removed perpendicularly to the symmetry axis.