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Given a configuration of pebbles on the vertices of a graph G, a pebbling move removes two pebbles from a vertex and puts one pebble on an adjacent vertex. The pebbling number of a graph G is the smallest number of pebbles required such that, given an arbitrary initial configuration of pebbles, one pebble can be moved to any vertex of G through some sequence of pebbling moves. Through constructing a non-tree weight function for Q 4 , we improve the weight function technique, introduced by Hurlbert and extended by Cranston et al., that gives an upper bound for the pebbling number of graphs. Then, we propose a conjecture on weight functions for the n-dimensional cube. We also construct a set of valid weight functions for variations of lollipop graphs, extending previously known constructions. [ABSTRACT FROM AUTHOR]

Abstract Background The aim of this project is to evaluate public contributors’ experiences of their involvement in qualitative data analysis workshops during an on-going research project titled ‘Personalised Primary care for Patients with Multiple long-term conditions’. Methods Four qualitative data analysis workshops were designed and conducted between August and December 2023. We used the Cube evaluation framework (henceforth referred to as the Cube) to evaluate the workshops. The Cube suggests four domains for successful PPI (voice, agenda, change, contribute).Within Workshops One, Two and Three public contributors had to login to an account to access the Cube; this was modified in Workshop Four following feedback from public contributors. Findings Across the four workshops the Cube was completed 11 times. Across all four workshops, public contributors thought that their voice was heard, that there were diverse ways to contribute and that they led the agenda. Public contributors thought that researchers responded to their questions and issues, when necessary. Conclusion This evaluation has shown that public contributors can gain new skills and lead qualitative data analysis discussions.

Any collection of non-blocking cubes, whose total volume does not exceed 1/3, can be packed into the unit cube. [ABSTRACT FROM AUTHOR]

Precise point positioning (PPP) is a prevalent, high-precision spatial absolution positioning method, and its performance can be enhanced by ambiguity resolution (AR). To fulfill the growing need for high-precision positioning, we developed an open-source GNSS data processing package based on the decoupled clock model called Cube, which integrates decoupled clock offset estimation and precise point positioning with ambiguity resolution (PPP-AR). Cube is a secondary development based on RTKLIB. Besides the decoupled clock model, Cube can also estimate legacy clocks for the International GNSS Service (IGS), as well as clocks with satellite code bias extraction, and perform PPP-AR using the integer-recovered clock model. In this work, we designed satellite clock estimation and PPP-AR experiments with one week of GPS data to validate Cube's performance. Results show that the software can produce high-precision satellite clock products and positioning results that are adequate for daily scientific study. With Cube, researchers do not need to rely on public PPP-AR products, and they can estimate decoupled clock products and implement PPP-AR anytime. [ABSTRACT FROM AUTHOR]

Atomically precise nanoclusters hold promise for supramolecular assembly and (opto)electronic‐ as well as magnetic materials. Herein, this work reports that treating palladium(0) precursors with a triphosphirane affords strongly colored Pd8(PDip)6 that is fully characterized by mass spectrometry, heteronuclear and Cross‐Polarization Magic‐Angle Spinning (CP‐MAS) NMR‐, infrared (IR), UV–vis, and X‐ray photoelectron (XP) spectroscopies, single‐crystal X‐Ray diffraction (sc‐XRD), mass spectrometry, and cyclovoltammetry (CV). This coordinatively unsaturated 104‐electron Pd(0) cluster features a cubic Pd8‐core, µ4‐capping phosphinidene ligands, and is air‐stable. Quantum chemical calculations provide insight to the cluster's electronic structure and suggest 5s/4d orbital mixing as well as minor Pd─P covalency. Trapping experiments reveal that cluster growth proceeds via insertion of Pd(0) into the triphosphirane. The unsaturated cluster senses ethylene and binds isocyanides, which triggers the rearrangement to a tetrahedral structure with a reduced frontier orbital energy gap. These experiments demonstrate facile cluster manipulation and highlight non‐destructive cluster rearrangement as is required for supramolecular assembly. [ABSTRACT FROM AUTHOR]

In this paper, we present the first nontrivial lower bound on the translative covering density of tetrahedra. To this end, we show the lower bound, in any translative covering of tetrahedra, on the density relative to a given cube. The resulting lower bound on the translative covering density of tetrahedra is 1 + 1.227 × 10 - 3 . [ABSTRACT FROM AUTHOR]

This work delves into the significant advancements in epidemiological modeling and public health policy driven by detailed, quantitative analyses of COVID‐19 aerosol transmission utilizing the capabilities of the supercomputer Fugaku, the world's fastest supercomputer in 2020. By integrating novel computational fluid dynamics (CFD) techniques integrated in the multi‐physics solver CUBE, we achieved scalable, high‐resolution simulations essential for modeling micrometer‐sized virus‐containing aerosols, revolutionizing our understanding of transmission risks in various societal contexts. This innovation significantly reduced the time‐to‐solution for these intricate simulations and allowed for the quick creation of digital twins that captured a broad range of social scenarios with substantial transmission risks. These efforts required a significant amount of computational resources, which were provided for through Fugaku, during COVID‐19. The detailed transmission risk assessments that were produced through this work had a significant impact on public health policies and public behavior throughout Japan, exemplifying a pivotal shift in the digital transformation of epidemiology and the proactive management of pandemic‐related challenges. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

While headsets dedicated to mixed reality are increasingly considered to virtualize workspaces in the office, the keyboard remains mostly unchanged and nevertheless is still envisioned as an interface for common professional activities heavily demanding in text entry. However, unlike headsets, a keyboard is intrinsically limited to immobile context during its use, due to the need for physical support. In this article, we investigate a radical change in the structural shape of the keyboard, switching from the plane to a cube, allowing users to fully benefit from their whole environment by entering text in a much wider variety of contexts. We designed a cubic layout based on the QWERTY and results from two user studies to define the best holding position as well as fingers preferences and reachability to the cubic shape. Then, we conducted two subsequent user studies and one longitudinal case study to compare and evaluate typing skill transfer from the keyboard, learning curve, fingers usage, usability, and workload in various contexts. The cubic-shaped text entry device finally showed its versatility with users having similar performances while standing with a mixed-reality headset or sitting in front of a laptop, and an input speed from an expert reaching 55.1 wpm. [ABSTRACT FROM AUTHOR]

Any collection of non-blocking four-dimensional cubes, whose total volume does not exceed 17/81, can be packed into the unit four-dimensional cube. This bound is tight for the parallel packing. [ABSTRACT FROM AUTHOR]

We prove that for any and any trigonometric polynomial with frequencies in the set one has with implied constant being absolute. We also show that the set is a Sidon set. [ABSTRACT FROM AUTHOR]

Abstract Atomically precise nanoclusters hold promise for supramolecular assembly and (opto)electronic‐ as well as magnetic materials. Herein, this work reports that treating palladium(0) precursors with a triphosphirane affords strongly colored Pd8(PDip)6 that is fully characterized by mass spectrometry, heteronuclear and Cross‐Polarization Magic‐Angle Spinning (CP‐MAS) NMR‐, infrared (IR), UV–vis, and X‐ray photoelectron (XP) spectroscopies, single‐crystal X‐Ray diffraction (sc‐XRD), mass spectrometry, and cyclovoltammetry (CV). This coordinatively unsaturated 104‐electron Pd(0) cluster features a cubic Pd8‐core, µ4‐capping phosphinidene ligands, and is air‐stable. Quantum chemical calculations provide insight to the cluster's electronic structure and suggest 5s/4d orbital mixing as well as minor Pd─P covalency. Trapping experiments reveal that cluster growth proceeds via insertion of Pd(0) into the triphosphirane. The unsaturated cluster senses ethylene and binds isocyanides, which triggers the rearrangement to a tetrahedral structure with a reduced frontier orbital energy gap. These experiments demonstrate facile cluster manipulation and highlight non‐destructive cluster rearrangement as is required for supramolecular assembly.

Single crystallization of LiNixCoyMn1‐x‐yO2(NCM) is currently an effective strategy to improve the cycling life of NCM cathode, owing to the reduced surface area and enhanced mechanical strength, but the application of single crystal NCM(SC‐NCM) is being hindered by severe particle agglomeration and poor C‐rate performance. Here, a strategy of three‐section‐sintering(TSS) with the presence of grain‐growth inhibitor was proposed, in which, the TSS includes three sections of phase‐formation, grain‐growth and phase‐preservation. While, the addition of MoO3 inhibits the grain growth and restrains the particle agglomeration. With the help of TSS and 1 mol % of MoO3, highly dispersed surface Mo‐doped SC‐NCM(MSC‐NCM) cubes are obtained with the average diameter of 1.3 μm. Benefiting from the surface Mo‐doping and the reduced surface energy, the Li+‐migration preferred (1 0 4) crystalline facet is exposed as the dominant plane in MSC‐NCM cubes, because of which, C‐rate performance is significantly improved compared with the regular SC‐NCM. Furthermore, this preparation strategy is compatible well with the current industrial production line, providing an easy way for the large‐scale production of SC‐NCM. [ABSTRACT FROM AUTHOR]

The ability of phase change materials (PCM) to store thermal energy has gained wide application area, like battery thermal management, solar water desalination and many other. The melting process of beeswax phase change material within the cube geometry with constant wall temperature (65 °C) boundary condition has been investigated using solidification and melting model. The fluid flow and heat transfer governing equations are solved using second order finite volume scheme. A PRESTO algorithm is applied for pressure-velocity coupling. The convergence criteria of 10−10 have been selected for energy equation, while 10−8 is selected for both momentum and continuity equations. The results like percentage variation along length-height and height-width plane for transient liquid fraction and temperature has been plotted, along with velocity streamlines within the cube geometry. From the obtained results it is concluded that the melting fraction and temperature of beeswax PCM is different in different planes and the major factors which affect the complete melting process is wall temperature, and the geometry. A difference of more than 0.1 °C in temperature has been recorded between mid-length-height and height-width plane while a difference of more than 2% in liquid fraction of PCM is observed. Even the uniformity of temperature and liquid fraction is notably influenced and vary along length, height, and width of cube geometry. Thus, it is concluded that melting process of PCM may affect the ability to store and release the heat energy which further affect the performance parameters of applied physical system.

Precise point positioning (PPP) is a prevalent, high-precision spatial absolution positioning method, and its performance can be enhanced by ambiguity resolution (AR). To fulfill the growing need for high-precision positioning, we developed an open-source GNSS data processing package based on the decoupled clock model called Cube, which integrates decoupled clock offset estimation and precise point positioning with ambiguity resolution (PPP-AR). Cube is a secondary development based on RTKLIB. Besides the decoupled clock model, Cube can also estimate legacy clocks for the International GNSS Service (IGS), as well as clocks with satellite code bias extraction, and perform PPP-AR using the integer-recovered clock model. In this work, we designed satellite clock estimation and PPP-AR experiments with one week of GPS data to validate Cube’s performance. Results show that the software can produce high-precision satellite clock products and positioning results that are adequate for daily scientific study. With Cube, researchers do not need to rely on public PPP-AR products, and they can estimate decoupled clock products and implement PPP-AR anytime.

This article presents the cracking and load-bearing behaviour of carbon-reinforced prismatic concrete tensile specimens. Grids with different geometries and impregnations were used as carbon reinforcement. In addition, the roving surfaces were partially coated with a fine sand to improve the bond between concrete and reinforcement. The article shows the influence of the different parameters on the developing cracks with respect to their width and spacing from each other. The material properties and tensile strengths of carbon concrete are also presented. These can be used for calculations. A fine-grained, commercially available shotcrete was used for the investigations. Based on the tests and results described in this article, an influence of the sanded carbon grids on the crack properties (crack widths, crack spacing) could be shown in comparison to unsanded carbon grids. [ABSTRACT FROM AUTHOR]

Before the movement Tendenza in 1973, Aldo Rossi and his collaborator Gianugo Polesello examined cubic components. In the early 1960s, they co-founded Studio di Architettura (SDA) and designed "Centro direzionale di Torino" and "Monument for the Resistance in Cuneo", which are now known as "Rossi's earliest work". This essay selects 13 cubic architectures designed by Polesello and Rossi, making 3D models with cubic proportions. From the definition of "transparency" of Colin Rowe, three tendencies of transparency are categorized: "literal cube", "phenomenal cube" and "fluctuating cube". To explain their difference, Polesello prefers a "literal cube" along a rationalistic 3D cube grid, while Rossi prefers a "phenomenal cube" with triangular components on the façade. Judging from three representations of the cube, the two intended the concept of the "Invisible Cube" in their architectural design. [ABSTRACT FROM AUTHOR]

Purpose: Accurate assessment of dural sinus, deep and cortical venous thrombosis on MR imaging is challenging. The aim of this study is to evaluate the accuracy of 3D-T1 turbo spin echo (T1S), sequences in detecting venous thrombosis and comparing it with susceptibility-weighted imaging (SWI), magnetic resonance venography (MRV) and post contrast T1 magnetization-prepared rapid acquisition gradient echo (T1C). Methods: A blinded retrospective observational analysis of 71 consecutive patients evaluated for cerebral venous thrombosis (CVT) and 30 control patients was performed. Multimodality reference standard adopted included T1C, SWI with MRV. Sub-analyses in superficial, deep and cortical venous segments were performed in addition to correlation of signal intensity of thrombus with the clinical stage. Results: A total of 2222 segments in 101 complete MRI examinations were evaluated. Sensitivity/specificity/positive predictive value/negative predictive value/accuracy and precision of T1S for detection of cortical vein thrombosis was 0.994/1/1/0.967/0.995/1, 1/0.874/0.949/1/0.963/0.950 for detection of superficial venous sinus thrombosis and 1/1/1/1/1/1 for deep venous thrombosis. The AUC yield for T1S was 0.997 for cortical, 1 for deep and 0.988 for superficial venous segments. Conclusion: T1S paralleled the accuracy of conventional sequences in the overall detection of CVT but showed superior accuracy in the detection of cortical venous thrombosis. It makes a fitting addition to the CVT MRI protocol in scenarios demanding negation of gadolinium administration. [ABSTRACT FROM AUTHOR]

Rigid origami has great potential in aerospace applications, especially deployable polyhedrons with one degree of freedom (DOF) and flat-foldability, whose types are few to date. In this paper, we create a novel foldable cube and a rhombic dodecahedron by introducing slits and diagonal creases to the surfaces, whose one-DOF rigid and flat-foldable properties are verified by kinematic analysis. Then, based on the isohedral quadrilateral transform, we project the creases and slits of the rhombic dodecahedron onto a tetrahedron to obtain a novel foldable tetrahedron that has two flat-foldable motion paths due to the existence of collinear creases. Following the second path, unnecessary creases are removed, and an origami tetrahedron with simplified creases is constructed. Both origami tetrahedrons possess a small folded area. Kinematic analysis reveals that these newly discovered origami polyhedrons are flat-foldable with one DOF, demonstrating favorable application prospects for space architectures and extraterrestrial habitats. [ABSTRACT FROM AUTHOR]

Among the didactic tools used in working with preschool children, one of the most prevalent and beloved is the cube. The cube is a favorite toy for children of all ages, as it offers countless possibilities for play. Its significance is reflected in its wide application in games for implementing activities of various content, and in arousing children's interest in developing and acquiring concepts that are being taught. Playing with cubes encourages children to be active participants and collaborators with adults in activities to the extent that the cube facilitates the discovery, deeper experience, and understanding of what is being learned. This paper presents various aspects of the cube as a concept; a geometric shape; a play prop; and a powerful didactic tool in the realization of preschool mathematical education.

In this paper we study the pair difference cordial labeling behavior of some trees and some graphs derived from cube graph. [ABSTRACT FROM AUTHOR]

Purpose: This study compares the performance of a 4-min multi-echo in steady-state acquisition (MENSA) with a 6-min fast spin echo with variable flip angle (CUBE) protocol for the assessment of lumbosacral plexus nerve root lesions. Methods: Seventy-two subjects underwent MENSA and CUBE sequences on a 3.0-T MRI scanner. Two musculoskeletal radiologists independently assessed the images for quality and diagnostic capability. A qualitative assessment scoring system for image quality and quantitative nerve signal-to-noise ratio (SNR) and iliac vein and muscle contrast-to-noise ratios (CNR) was applied. Using surgical reports as the reference, sensitivity, specificity, accuracy, and area under the receiver operating characteristic curves (AUC) were evaluated. Intraclass correlation coefficients (ICC) and weighted kappa were used to calculate reliability. Results: MENSA image quality rating (3.679 ± 0.47) was higher than for CUBE images (3.038 ± 0.68), and MENSA showed higher mean nerve root SNR (36.935 ± 8.33 vs. 27.777 ± 7.41), iliac vein CNR (24.678 ± 6.63 vs. 5.210 ± 3.93), and muscle CNR (19.414 ± 6.07 vs. 13.531 ± 0.65) than CUBE (P < 0.05). Weighted kappa and ICC values indicated good reliability. Sensitivity, specificity, and accuracy of diagnosis based on MENSA images were 96.23%, 89.47%, and 94.44%, respectively, and AUC was 0.929, compared with 92.45%, 84.21%, 90.28%, and 0.883 for CUBE images. The two correlated ROC curves were not significantly different. Weighted kappa values for intraobserver (0.758) and interobserver (0.768–0.818) reliability were substantial to perfect. Conclusion: A time-efficient 4-min MENSA protocol exhibits superior image quality and high vascular contrast with the potential to produce high-resolution lumbosacral nerve root images. [ABSTRACT FROM AUTHOR]

Let 0 < q ≤ p ≤ ∞ , r ∈ (0 , ∞ ] , and M q , r p (R n) denote the Bourgain–Morrey space which was introduced by J. Bourgain and has proved important in the study of some linear and nonlinear partial differential equations. In this article, via cleverly combining both the structure of Bourgain–Morrey spaces and the structure of Triebel–Lizorkin spaces and adding an extra exponent τ ∈ (0 , ∞ ] , the authors introduce a new class of function spaces, called Triebel–Lizorkin–Bourgain–Morrey spaces M F ˙ q , r p , τ (R n) . The authors show that M F ˙ q , r p , τ (R n) is just a bridge connecting Bourgain–Morrey spaces and global Morrey spaces. In addition, by fully using exquisite geometrical properties of cubes of Euclidean spaces, the authors also explore various fundamental real-variable properties of M F ˙ q , r p , τ (R n) as well as its relations with other Morrey type spaces, such as Besov–Bourgain–Morrey spaces and local Morrey spaces. Finally, via finding an equivalent quasi-norm of Herz spaces and making full use of both the Calderón product and the sparse family of dyadic grids, the authors obtain the sharp boundedness on M F ˙ q , r p , τ (R n) of classical operators including the Hardy–Littlewood maximal operator, the Calderón–Zygmund operator, and the fractional integral. [ABSTRACT FROM AUTHOR]

Copyright of Acta Prataculturae Sinica is the property of Acta Prataculturae Sinica Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Shrinkage tests for a jointless 24.4 m long carbon concrete shell – approval procedure for the TWIST shells For the construction of the carbon reinforced concrete house CUBE, extensive investigations were necessary as a prerequisite for obtaining of approvals in individual cases (ZiE) and project‐related type approvals (vBG). Material parameters of non‐regulated building materials, new areas of application of already approved building products and non‐standard construction methods were regulated. In the first part, we explain how the shrinkage values of the concretes for the load‐bearing and weather shells of the TWIST elements were determined. The second part deals with the shrinkage behavior of two 24.4 m long slab strips that represent a section of the equally long TWIST element. The investigations allowed for predictions about the deformation behavior of the carbon reinforced concrete weather shell. Based on the values measured experimentally or determined by model calibration and finally recorded in the ZiE/vBG, the deformations of the carbon reinforced concrete shells in the serviceability limit state could be determined realistically by calculation. The values were so low that the shells could be produced on site without joints. [ABSTRACT FROM AUTHOR]

CUBE Project introduction The CUBE project was successful in developing and producing slender, load‐bearing and thermally insulated carbon concrete components as well as designing, verifying, approving and implementing the world's first complete building in carbon concrete construction. The design of CUBE combines both free‐form and flat components to demonstrate the broad applicability of carbon concrete. Over the next few years, the building will be extensively investigated, with a particular focus on testing and evaluating the structural‐physical characteristics, the serviceability and durability as well as its visual quality. This means that the current state of development in carbon concrete construction can now be presented to those with professional interest as well as to the general public. Further insights into the long‐term behaviour of the building material can be gained and the experiences and developments from the project can be used for future carbon concrete buildings. [ABSTRACT FROM AUTHOR]

Life cycle analysis of newly developed carbon concrete building components The CUBE building represents the research results of the whole C3‐project with many new building elements, materials, and construction designs. The article analyses the ecological sustainability of some building elements, although structural, engineering, and in part even financial aspects were more important during design and construction of the building. For specific wall and ceiling elements, a life cycle analysis following EN 15804 was performed. For the results are compared with those of typical steel reinforced concrete building elements. The curved element TWIST no such comparison exists. In this article, a representative section of the TWIST is analysed and the results presented for 1 m2. Overall, the environmental impacts of the newly developed building elements are comparable with current steel reinforced concrete constructions. Contrasting those, carbon concrete offers substantial potentials for short‐term improvements in environmental impacts. [ABSTRACT FROM AUTHOR]

Precast construction with carbon reinforced concrete and aerogel thermal insulation The CUBE BOX represents a milestone in the development of carbon reinforced concrete. For the first time, an industrially manufactured building is made of carbon reinforced concrete. Within the scope of the construction project, steel reinforced (semi‐)precast concrete elements were transferred into the carbon concrete technology. The article also describes the integration of aerogel thermal insulation in semi‐precast concrete construction. Based on various design problems, the production and assembly of the (semi‐)precast walls and the precast ceilings are described. A particular challenge of the project is the use of an automated production line in the precast concrete plant. From a practical point of view, the essential work steps are described in detail. [ABSTRACT FROM AUTHOR]

Initial building physics investigations in the planning phase of the CUBE During the planning and development of the CUBE, its aspects of building physics were analyzed. Various mathematical and experimental studies were done in advance as well as simulations of the energy demand according to DIN V 18599. The passive house standard aimed for in the planning process could not be realized. Measurements of the airborne sound insulation of the TWIST component structure in a sound test rig showed no sound decoupling of the 4 cm thick weather shell. Furthermore, room acoustic simulation calculations showed that the hard surfaces of the exposed concrete walls and the exposed concrete ceilings as well as the floor and the glass facade would lead to unfavorable acoustics with long reverberation times. For the development of a moisture protection concept, various theoretical examinations and investigations were carried out. [ABSTRACT FROM AUTHOR]

In this paper, we study the rank characteristics for families of cubic theories, as well as new properties of cubic theories as pseudofiniteness and smooth approximability. It is proved that in the family of cubic theories, any theory is a theory of finite structure or is approximated by theories of finite structures. The property of pseudofiniteness or smoothly approximability allows one to investigate finite objects instead of complex infinite ones, or vice versa, to produce more complex ones from simple structures.

Let p,q∈[1,∞], α∈ℝ, and s be a nonnegative integer. In this article, the authors introduce a new function space JN˜(p,q,s)α(X) of John–Nirenberg–Campanato type, where X denotes ℝn or any cube Q0 of ℝn with finite edge length. The authors give an equivalent characterization of JN˜(p,q,s)α(X) via both the John–Nirenberg–Campanato space and the Riesz–Morrey space. Moreover, for the particular case s=0, this new space can be equivalently characterized by both maximal functions and their commutators. Additionally, the authors give some basic properties, a good‐ λ inequality, and a John–Nirenberg‐type inequality for JN˜(p,q,s)α(X). [ABSTRACT FROM AUTHOR]

The methodological details of the indirect analytical determination of the thickness of the diamond powder coating, which is an important characteristic of the latter, are analyzed. The key role of the method used for matching the actual geometric parameters of the grain to the parameters of its adopted 3D model as a factor that has an effect on the error in determining the thickness of the coating is proven. The results of a comparative study of the effect of the method of matching the actual geometric parameters of the test grain (cuboctahedron) to the parameters of its accepted 3D models (sphere, cube, and ellipsoid) on the thickness of the coating and the error of its determination are given. [ABSTRACT FROM AUTHOR]

The author discusses the relationship between the structure of Bulienkov's T-knot and ring geological structures on the Earth's surface that have formed over eons. The positions of atoms in Bulienkov's T‑knot correspond to the vertices of Platonic solids: two tetrahedra, an icosahedron, and an octahedron (27 positions in total, including the central one). If we place the central atom of Bulienkov's T-knot at the center of a sphere (geoid) and project the remaining positions radially onto its surface, we can restore the classical ring structures known in geology on its surface using the projections as centers. Bulienkov's T-knot allows us to obtain not only a clear hierarchical relationship between the icosahedral, octahedral, and tetrahedral models of the Earth's ring structures, but to identify/confirm critical zones on the Earth known for anomalous geological structures and processes as well. [ABSTRACT FROM AUTHOR]

[Display omitted] • Non-canonical polyT-MA supramolecular structures respond to five external stimuli. • Multi-stimuli-responsive DNA hydrogels bridged by the supramolecules are developed. • PolyT-MA acts as supramolecular glue to engineer macroscopic hydrogel blocks. • Reprogrammable LEGO constructs are achieved. The arbitrary, modular, and reprogrammable engineering of macroscopic objects by DNA interactions remains a challenge, despite the well-established use of DNA to drive constructs at nano/micro-scale. Moreover, achieving adaptive responsiveness in assembled architectures under dynamic environmental triggers has yet to be realized. In this study, we introduce the association of oligo-thymine strands (polyT) and melamine (MA), as a low-molecular-weight cofactor, into a supramolecular DNA duplex, termed polyT-MA nanobridge. This unique nanostructure exhibits responsiveness to five external stimuli, including temperature, DNA strand, small molecule, acidic pH, and alkaline pH. The polyT-MA nanobridge is developed as the dynamic crosslinking elements for constructing multi-stimuli responsive DNA hydrogels, which exhibit physiochemical properties changes (e.g., rigidity, thermal stability) and hydrogel-to-liquid phase transitions in response to the five external triggers. Notably, the assembly of macroscopic hydrogel blocks at millimeter scale (cubes in 5 × 5 × 5 mm dimensions) into diverse architectures, e.g., linear type, cross, P-shape, T-shape, or heteromorphy, is achieved by using the non-canonical supramolecular polyT-MA nanobridges. Sequential, dynamic, and selective disassembly of polyT-MA bridged hydrogel constructs is triggered by multiple external stimuli and the rearrangement of these separated individual cubes into other architectures in LEGO styles is presented. This study provides insights into the development of advanced materials and devices with reconfigurable architectures and functionalities for intelligent nanoengineering applications. [ABSTRACT FROM AUTHOR]

This article presents the cracking and load-bearing behaviour of carbon-reinforced prismatic concrete tensile specimens. Grids with different geometries and impregnations were used as carbon reinforcement. In addition, the roving surfaces were partially coated with a fine sand to improve the bond between concrete and reinforcement. The article shows the influence of the different parameters on the developing cracks with respect to their width and spacing from each other. The material properties and tensile strengths of carbon concrete are also presented. These can be used for calculations. A fine-grained, commercially available shotcrete was used for the investigations. Based on the tests and results described in this article, an influence of the sanded carbon grids on the crack properties (crack widths, crack spacing) could be shown in comparison to unsanded carbon grids.

In this article, the authors refer to the interesting nature and properties of the number 24 and its occurrence and relevance in different contexts and conjecture that it is the raison d’ˆetre for its occurrence in the definition of the τ -function of Ramanujan. [ABSTRACT FROM AUTHOR]

We study the John-Nirenberg space J N p , which is a generalization of the space of bounded mean oscillation. In this paper we construct new J N p functions, that increase the understanding of this function space. It is already known that L p (Q 0) ⊊ J N p (Q 0) ⊊ L p , ∞ (Q 0) . We show that if | f | 1 / p ∈ J N p (Q 0) , then | f | 1 / q ∈ J N q (Q 0) , where q ≥ p , but there exists a nonnegative function f such that f 1 / p ∉ J N p (Q 0) even though f 1 / q ∈ J N q (Q 0) , for every q ∈ (p , ∞) . We present functions in J N p (Q 0) \ V J N p (Q 0) and in V J N p (Q 0) \ L p (Q 0) , proving the nontriviality of the vanishing subspace V J N p , which is a J N p space version of VMO. We prove the embedding J N p (R n) ⊂ L p , ∞ (R n) / R . Finally we show that we can extend the constructed functions into R n , such that we get a function in J N p (R n) \ V J N p (R n) and another in C J N p (R n) \ L p (R n) / R . Here C J N p is a subspace of J N p that is inspired by the space CMO. [ABSTRACT FROM AUTHOR]

Our goal is to discuss the different issues that arise when attempting to visualize a joints-and-bars cube through GeoGebra, a widespread program that combines dynamic geometry (DGS) and computer algebra systems (CAS). As is standard in the DGS framework, the performance of the graphic model (i.e., the positions of the other vertices when dragging a given one) must correspond to a mathematically rigorous, symbolic computation-driven output. This requirement poses both computational algebraic geometry and dynamic geometry programming challenges that will be described, together with the corresponding proposed solutions. Among these, we include a complete determination of the dimension of the cubic linkage from an algebraic perspective, and introduce advanced 3D visualizations of this structure by using the GeoGebra software. [ABSTRACT FROM AUTHOR]

Copyright of Hydrographic Surveying & Charting / Haiyang Cehui is the property of Hydrographic Surveying & Charting Editorial Board and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)