Space Frame Research Articles

3-Boyutlu Öklid Uzayında Adjoint Eğrilerin Binormal Yüzeyleri

In this study, we make a specific contribution to the subject of surfaces with wide application areas defined with the help of associated curves. In particular, we examine the binormal surfaces generated via adjoint curves which are one of the important examples of associated curves. By defining the binormal surfaces of adjoint curves under the Frenet-Serret (FS) frame in 3D Euclidean space, we characterize such surfaces and give some results with the aid of these characterizations.

Individual Locating of Soccer Players from a Single Moving View.

Positional data in team sports is key in evaluating the players' individual and collective performances. When the sole source of data is a broadcast-like video of the game, an efficient video tracking method is required to generate this data. This article describes a framework that extracts individual soccer player positions on the field. It is based on two main components. As in broadcast-like videos of team sport games, the camera view moves to follow the action and a sport field registration method estimates the homography between the pitch and the frame space. Our method estimates the positions of key points sampled on the pitch thanks to an encoder-decoder architecture. The attention mechanisms of the encoder, based on a vision transformer, captures characteristic pitch features globally in the frames. A multiple person tracker generates tracklets in the frame space by associating, with bipartite matching, the player detections between the current and the previous frames thanks to Intersection-Over-Union and distance criteria. Tracklets are then iteratively merged with appearance criteria thanks to a re-identification model. This model is fine-tuned in a self-supervised way on the player thumbnails of the video sample to specifically recognize the fine identification details of each player. The player positions in the frames projected by the homographies allow the obtaining of the real position of the players on the pitch at every moment of the video. We experimentally evaluate our sport field registration method and our 2D player tracker on public datasets. We demonstrate that they both outperform previous works for most metrics. Our 2D player tracker was also awarded first place at the SoccerNet tracking challenge in 2022 and 2023.

Assessment System for Child Head Injury from Falls Based on Neural Network Learning.

Toddlers face serious health hazards if they fall from relatively high places at home during everyday activities and are not swiftly rescued. Still, few effective, precise, and exhaustive solutions exist for such a task. This research aims to create a real-time assessment system for head injury from falls. Two phases are involved in processing the framework: In phase I, the data of joints is obtained by processing surveillance video with Open Pose. The long short-term memory (LSTM) network and 3D transform model are then used to integrate key spots' frame space and time information. In phase II, the head acceleration is derived and inserted into the HIC value calculation, and a classification model is developed to assess the injury. We collected 200 RGB-captured daily films of 13- to 30-month-old toddlers playing near furniture edges, guardrails, and upside-down falls. Five hundred video clips extracted from these are divided in an 8:2 ratio into a training and validation set. We prepared an additional collection of 300 video clips (test set) of toddlers' daily falling at home from their parents to evaluate the framework's performance. The experimental findings revealed a classification accuracy of 96.67%. The feasibility of a real-time AI technique for assessing head injuries in falls through monitoring was proven.

Very High Cycle Fatigue Properties and Damage Evolution in Al-Si Cast Alloys

Abstract The steady progress in electro mobility increases the demand for lightweight space frame and engine solutions. Advanced aluminum-silicon cast alloys with additions of magnesium, copper, or both for precipitation hardening are promising candidates for lightweight structures because of their high strength-to-weight ratio. For a reliable design, the fatigue performance in the very high cycle fatigue (VHCF) regime must be understood. Therefore, this study deals with the influence of frequency on VHCF properties as well as fatigue damage evolution in AlSi7Mg and AlSi10Mg sand-cast alloys. The VHCF tests were performed using a resonant (70 Hz), a high-frequency resonant (1 kHz), and an ultrasonic (20 kHz) fatigue testing system. Thereby, a significant frequency effect could be determined that resulted in an increased fatigue lifetime by 1 decade at 1 kHz and by 2 decades at 20 kHz, whereas no significant change in fatigue limit could be determined. Moreover, the fatigue crack initiation mechanisms change from surface crack initiation at 70 Hz and 1 kHz to volume crack initiation at 20 kHz. Using the defect-based Murakami approach, including a lightweight extension of Noguchi, a defect-induced (size, location) frequency effect could be excluded. Based on damage monitoring, the effect could be related to the crack propagation phase, which is accelerated at low frequencies (<100 Hz) because of a humidity reaction with the fatigue crack surface and the formation of atomic hydrogen resulting in a saturated hydrogen embrittlement per cycle. At high frequencies of 1 kHz and 20 kHz, no saturated hydrogen embrittlement per cycle can be reached.

On matrix-valued Gabor frames over locally compact abelian groups

In this paper, we study Gabor frames in the matrix-valued signal space [Formula: see text], where [Formula: see text] is a locally compact abelian group which is metrizable and [Formula: see text]-compact, and [Formula: see text] is a positive integer. First, we give sufficient conditions on scalars in an infinite combination of vectors (from a given matrix-valued Gabor frame) to constitute a new frame for the space [Formula: see text]. This generalizes a result due to Aldroubi. Second, we discuss frame conditions for finite sums of matrix-valued Gabor frames. Sufficient conditions for finite sums of matrix-valued Gabor frames in terms of frame bounds are established. It is shown that the sum of images of matrix-valued Gabor frames under bounded linear operators acting on [Formula: see text] constitute a frame for the space [Formula: see text] provided operators are adjointable with respect to the matrix-valued inner product and satisfy a majorization. Finally, we show that matrix-valued Gabor frames are stable under small perturbations.

Generating and Characterization Loft Surface by Type-2-Bishop Frame in Isotropic Space

Generating and Characterization Loft Surface by Type-2-Bishop Frame in Isotropic Space

Corotational Finite Element Dynamic Analysis of Space Frames with Geometrically Nonlinear Behavior Based on Tait–Bryan Angles

The aim of this study is to compose a corotational finite element formulation for space frames with geometrically nonlinear behavior under dynamic loads. Using a moving frame through three successive rotations similar to Euler angles is one of the oldest techniques; however, there are still some gaps that require attention, mainly due to singularity. Hence, alternative techniques had been developed, sometimes elusive and computationally expensive. In this paper, we went back to the old technique and filled the gaps. Three-coordinate systems are used, i.e., the fixed global coordinate system, the fixed local coordinate system that is attached individually to every element, and the corotational local frame for each element that moves and rotates with the element. The deformation is always small relative to the corotational frame. The successive rotations between different coordinate systems are expressed using Tait–Bryan angles. Lagrange’s equation is used to derive the equation of motion, and the stiffness and mass matrices are obtained using the Euler–Bernoulli beam model. A MATLAB code is developed based on the Newton–Raphson method and the Newmark direct integration implicit method. In traditional techniques, singularity is attained when any rotation angle in the fixed local frame approaches π / 2 , and if any is greater than π / 2 , the techniques could fail to specify the location of the element. In this paper, each case is treated with a proper procedure, and special handling of trigonometric formulations prevents singularity and correctly specifies the location of elements in all situations. Different examples of beams and frames are analysed. While the method is not intricate, it is timesaving, is highly effective, provides more stable and robust analysis, and gives sufficiently accurate results. Compared to the parametrization of the finite rotations technique, the method has a significant reduction in the convergence rate because it avoids the storage of joint orientation matrices.

Reactivated fracture-controlled uranium mineralization: An example from NNE-SSW Kamaguttapalle–Kammapalle tract, Kadapa district, Andhra Pradesh, India

The Cuddapah Basin (CB) and its basement can be considered as an appropriate uranium metallogenic province. The basement complex of CB in the Eastern Dharwar Craton (EDC), India, has been the target for structurally controlled uranium exploration since the early 1980s. Most of the brittle-ductile deformation induced reactivated narrow linear fracture zones often exhibit significant surface and sub-surface uranium occurrence. There are about 10 fracture zones associated with uranium mineralization. Amongst them, the Kamaguttapalle–Kammapalle fracture zone (KKF) in the south of the CB is quite interesting from an exploration viewpoint with a suitable geologic setting in space and time frame. Geomorphic, structural and petro-mineralogic exploration guides imply the possibility of economic uranium concentration along the NNE-SSW trend where tectonic reactivation took place over pre-existing ductile shear zone. Progressive exhumation and transition from ductile to brittle deformation regime led to the development of dominant strike slip tectonics with an associated riedel fracture system, which are subsidiary coeval shear fractures used in depicting sense of movement. Intense illitization and hematitization are often observed. Quartz reefs and veins along the NNE-SSW trend cut the preexisting mylonites at places. About 9 stages of fracturing is observed out of which 3 stages are related to uranium mineralization. All the 9 deformations are related to strike slip tectonics which in turn is part of Grenville orogeny. Paragenetic sequence and mode of occurrences of uranium phases deciphers about the importance of low to moderate level epi‑meso type hydrothermal (100°–250 °C) fluids as carrier of U. Reactivated fractures and quartz veination also act as controlling factors of mineralization. Strain analysis points to positive and negative flower structures at different segments of the fracture zone. Based on the litho-structural attributes it is established that maximum compression (σ1) acted along the NNW-SSE direction. Fractured quartz veins provide well defined permeability and trapping facility by restricting transverse fluid movement as a mechanical barrier. The presented model gives an idea on role of strike-slip tectonics in uranium mineralization for narrowing down the target zone for sub-surface exploration.

‘I can easily switch to the Kazakh language, also to the Russian language’: reimagining Kazakhstani CLIL implementation as a third space

ABSTRACT There is extensive CLIL research on stakeholders’ practices, integration of content and language, and pedagogies. However, limited studies report on teachers’ pre-existing knowledge before CLIL implementation and how it influences their classroom pedagogy. Using a third space frame, this study examined CLIL implementation in Kazakhstan. It included 15 science teachers who teach science through the English medium of instruction (EMI). A hybrid coding strategy was followed to analyze questionnaires, teachers’ science lessons, multimodal teaching-based scenarios, and semi-structured interviews. Our findings revealed that teachers’ CLIL implementation was guided by their (1) hybrid beliefs about scientific knowledge and learning, (2) humanising pedagogy, (3) shift to constructivist science pedagogy, and (4) hybrid linguistic stance. We conclude that a third-space perspective diverts the gaze from CLIL teachers’ challenges to illuminate the entanglement of teachers’ epistemic stance, pedagogical content knowledge (PCK), and linguistic stance as emergent discursive practices when policy borrowings connect global and local epistemologies.

New aspects of weaving K-frames: the excess and duality

Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems in distributed signal processing and wireless sensor networks. Likewise weaving K -frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator K. In this paper, we study the notion of weaving and its connection to the duality of K-frames and construct several pairs of woven K-frames. Also, we find a unique biorthogonal sequence for every K-Riesz basis and obtain a $K^*$-frame which is woven by its canonical dual. Moreover, we describe the excess for K-frames and prove that any two woven K-frames in a separable Hilbert space have the same excess. Finally, we introduce the necessary and sufficient condition under which a K-frame and its image under an invertible operator have the same excess.

Generalized stimulated Raman scattering with nonlocal effects

We present a generalized quantum theory of stimulated Raman scattering, which is based on coupled Heisenberg–Langevin equations. Analytical solutions in previous models neglect the effects of the frequency dispersion, assume far-off resonance and only consider slowly varying terms in the atomic operator. In obtaining the more general theory, we have derived partial integro-differential equation containing polarization kernels that include all the temporal nonlocal effects using systematic integral method over time. Analytical solutions of the Stokes field with greater generality for arbitrary spatial-temporal laser fields have been obtained using Laplace transform in the retarded space frame with minimal approximations made. The solutions are very general and potentially useful for studying systems in which highly accurate modeling is required such as quantum memories of a wide range of Raman systems.

Frame induced position shifts extend outside the frame in space but not in time

Frame induced position shifts extend outside the frame in space but not in time

Models of the Mediterranean, Camocio’s Isolario, and Early Modern Showings and Tellings in light of Lepanto

This essay proposes three models of Mediterranean space and action that emerge out of early modern narratives and visuals (particularly maps). These overlapping models, for the long sixteenth century, are: 1) itinerary; 2) empire; and 3) predator, all of which appear under the broader frame of geographic-commercial space that is either conflicted or pacific. I employ a preliminary narrative, The Deeds of Commander Pietro Mocenigo, by Coriolano Cippico, a galley commander in the Ottoman-Venetian conflict of 1470-1474; then, the isolario of Giovanni Camocio, as it appeared in the aftermath of the Battle of Lepanto in 1571. Camocio’s maps focus attention on that battle and on imperial conflict. But his vision of the Mediterranean is that of a range of familiar, maritime spaces dotted with fortresses and harbors, sometimes enmeshed in conflict and more often not.

Theoretical molecular spectroscopy of actinide compounds: the ThO molecule

The tiny-core generalised (Gatchina) relativistic pseudopotential (GRPP) model provides an accurate approximation for many-electron Hamiltonians of molecules containing heavy atoms, ensuring a proper description of the effects of non-Coulombian electron-electron interactions, electronic self-energy and vacuum polarisation. Combining this model with electron correlation treatment in the frames of the intermediate Hamiltonian Fock space coupled cluster theory employing incomplete main model spaces, one obtains a reliable and economical tool for excited state modelling. The performance of this method is assessed in applications to ab initio modelling of excited electronic states of the thorium monoxide molecule with term energies below 20,000 cm. Radiative lifetimes of excited states are estimated using truncated expansions of effective and metric operators in powers of cluster amplitudes.

Framing of space and place: an insight into George Town World Heritage Site, Penang, Malaysia

In architecture and urban design, the meaning, interpretations, identities, and uses of space and place are contentious topics. By framing space, which becomes a mechanism for the authorised group to manage power, it is possible to programme users’ activities regarding how to occupy space and location. This paper examines the construction of space and place in an urban, multicultural, and postcolonial World Heritage City. The qualitative research takes place at the George Town World Heritage Site (WHS) in Malaysia, specifically the ‘Street of Harmony’. The study contributes to a better understanding of the relationship between the World Heritage city and its local communities through field observations and semi-structured interviews with the communities. Policy (heritage and conservation and education), community-based, tourism, heritage, and politics are the identified frames. The street is portrayed in a number of ways, including the way in which a person’s daily activities are framed by the confines of their home. Understanding this contributes to the future practicable and nondisruptive practice of urban regeneration, resulting in a resilient and sustainable community.

Continuous frames in n-Hilbert spaces and their tensor products

We introduce the notion of continuous frame in n-Hilbert space which is a generalization of discrete frame in n-Hilbert space. The tensor product of Hilbert spaces is a very important topic in mathematics. Here we also introduce the concept of continuous frame for the tensor products of n-Hilbert spaces. Further, we study dual continuous frame and continuous Bessel multiplier in n-Hilbert spaces and their tensor products.

Generative design of space frames for additive manufacturing technology

A generative design methodology is presented that solves for minimum volume and compliance space-frame systems, with consideration of stress and buckling constraints. The solution space is explored using formal topology optimisation routines. A parameterisation method converts voxelised topology optimisation solutions into skeletonised connectivity representations. An inequality constrained gradient descent optimisation method optimises and defines cross-sectional geometry. This enables fast and automatic solution generation, providing designers with sets of high-performing problem solutions. Skeleton representations provide an inexpensive modelling tool for parallel analysis of physical problems difficult to model using topology optimisation. Geometry is represented using traditional engineering cross-sections with well understood behaviour. This improves certainty in the performance of solutions, simplifying certification processes. The generative design of a structural aerospace bracket for additive manufacture has been used as a case study within this research. A design of experiments produced 360 topology optimisation results, altering input variables and discretisation resolution to identify their effect on solution outcomes and the performance of parameterisation. The proposed method was found to robustly generate high-performing solutions utilising low-resolution topology optimisation. Additionally, 6 high-performing topologies were identified, providing designers with a set of solutions to select from. Limitations on the parameterisation process were identified, with topology optimisation solutions with volume fractions above 0.2 not parameterising successfully, and simulations with a resolution of 5 mm element size and below generating low performing skeletonised topologies.

Cyclic test and finite element analysis of a steel double K-braced frame with laterally-restrained plates for RC building retrofit

Damage was discovered in existing 24-story reinforced concrete (RC) buildings in New Taipei City under the 2015 Hualien earthquake with a magnitude of 6.3. A new scheme was proposed to retrofit the buildings by adding a steel concentrically double K-braced frame in a limited space, with diaphragm plates to laterally restrain each brace to increase its buckling strength. A cyclic test was first conducted on a full-scale steel braced frame specimen, composed of a steel boundary frame, two pairs of K-type-arranged plates for axially loaded braces, diaphragm plates for brace buckling restraint, and surrounding RC members. Secondly, a finite element (FE) analysis was conducted on the specimen for a correlation study and investigation of force transfer between the infilled braced frame and surrounding RC members. A finite element parametric study was then conducted on single braces with different numbers of restraint and plate thicknesses to investigate the cyclic behavior and buckling force. The AISC 360-16 (2016) provides a very conservative prediction of the brace bucking force, but the prediction based on Wolchuk (1963) reasonably matches well the test and FE analysis results. A cyclic backbone curve for a single brace modeling, considering in-plane lateral supports, was proposed in this work.

Some Generalizations of Relay Fusion Frames and F , G -Relay Fusion Frames in Hilbert C ∗ -Modules

The relay fusion frame proposed by Hong and Li is an extension of a fusion frame that has many applications in science. In this study, we introduce relay fusion frames in Hilbert C ∗ -modules very naturally and shift some common attributes of fusion frames and relay fusion frames in Hilbert spaces to relay fusion frames in Hilbert C ∗ -modules. In addition, we generalize some perturbation results in frame theory to relay fusion frames in Hilbert C ∗ -modules. Finally, we introduce a class of F , G -relay fusion frames as a generalization of K -frames and present some perturbation results for F , G -relay fusion frames in Hilbert C ∗ -modules.

An investigation on stiffened cold-formed steel unequal angle box section columns

Built-up box sections are gaining popularity as column members in cold-formed steel (CFS) construction. Applications include CFS trusses, space frames, and portal frames. Two identical CFS unequal angles are used in this article to form built-up rectangular angle box columns (BUABC). These BUABC, which can be plain or with stiffeners (longer and shorter legs), are grooved on the faces of the columns in the major and minor axis directions and connected with self-drilling screws (fasteners) through their lips. There are no reports in the literature on the advantages of stiffeners (longer and shorter legs) provided in BUABC. This paper presents 78 new results for the BUABC as plain and with stiffeners (longer and shorter legs), including 14 test results and 64 finite element (FE) results. The axial strengths of BUABC with two stiffeners in the longer leg and one stiffener in the shorter leg showed an increase of about 28% on average when compared to the axial strength of plain BUABC, according to the experimental results. The FEA-derived ultimate loads and failure modes are in good agreement with the experimental results. The verified FE model was then used in the parametric study to investigate the effect of stiffeners (longer and shorter legs) on the axial strength of BUABC. The parametric study considered two distinct geometries with two distinct lengths (300 mm and 600 mm). The axial strengths of the stub BUABC tested against the Direct Strength Method (DSM) prediction were conservative, up to 3% on average, while they were 13% conservative for the short BUABC. This shows that the DSM prediction was more conservative, with an increase in slenderness that was governed by the modified slenderness ratio. The DSM strength predictions were less conservative for the stub BUABC that failed due to local buckling, whereas the DSM strength predictions were more conservative for the short BUABC that failed due to a combination of local and flexural buckling.