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This article focuses on enhancing the range of motion (ROM) of the Tetra II joint, a spherical compliant joint consisting of three internally interconnected tetrahedron-shaped elements that achieve motion through elastic deformation. Despite its excellent precision, this specific design is constrained in terms of ROM due to internal contacts among the tetrahedral elements. To overcome this limitation, this study utilizes a computer-aided engineering (CAE) framework to optimize the configuration of the Tetra II joint and enhance its ROM. The resultant optimized joint, referred to as Tetra III, is subsequently compared to Tetra II in terms of both ROM and center shift. Finite element models (FEM) are employed to validate the optimization results and examine how various tetrahedron-shaped geometries impact the joint's performance. The newly optimized joint exhibits a significantly higher ROM compared to the previous version, while maintaining excellent precision and overall smaller dimensions. Finally, to demonstrate its manufacturability, the Tetra III joint is produced using selective laser sintering (SLS) technology, with Duraform PA serving as the construction material. The successful fabrication serves as a demonstrative example of the improved design of the Tetra III joint. [ABSTRACT FROM AUTHOR]

We prove a comparison theorem for certain types of polyhedra in a 3-manifold with its scalar curvature bounded below by -6. The result confirms in some cases the Gromov dihedral rigidity conjecture in hyperbolic 3-space. [ABSTRACT FROM AUTHOR]

Platinum catalysts with {111} surface has obvious advantages, but the control of {111} exposure usually requires surfactants which cover the surface and decrease the catalytic performance. In this paper, tetrahedral platinum nanoparticle catalysts were successfully prepared with a simple one-step hydrothermal method and their size were successfully controlled under sub-5 nm. The tetrahedral morphology was controlled through the decomposition of dimethylamine by DMF and the small size was determined by alcohol acid radical. Because of the profitable effect of the amines for the tetrahedral morphology, no surfactant was need during the preparation. The catalysis activity was assured by the tetrahedral morphology with Pt {111} exposure without the surfactant covering, and the small size further increased the number of activity sites. For HOR, the catalyst showed higher activity, stronger anti-CO poisoning performance and longer stability than those of commercial catalyst with the same platinum load. For ORR, the catalyst also showed better performances which further promoted the four-electron reaction. Our simple preparation method successfully achieved the aims of the morphology control, size control and the elimination of surfactant, which effectively assured the good catalyst performances. The simple preparation path of such good catalysts shows a great application potential. [ABSTRACT FROM AUTHOR]

Based on the geometric characteristics of a tetrahedron, quantitative estimates of its degeneracy are proposed and their relationship with the condition number of local bases generated by the edges emerging from a single vertex is established. The concept of the tetrahedron degeneracy index is introduced in several versions, and their practical equivalence to each other is established. To assess the quality of a particular tetrahedral partition, we propose calculating the empirical distribution function of the degeneracy index on its tetrahedral elements. An irregular model triangulation (tetrahedralization or tetrahedral partition) of three-dimensional space is proposed, depending on a control parameter that determines the quality of its elements. The coordinates of the tetrahedra vertices of the model triangulation tetrahedra are the sums of the corresponding coordinates of the nodes of some given regular mesh and random increments to them. For various values of the control parameter, the empirical distribution function of the tetrahedron degeneracy index is calculated, which is considered as a quantitative characteristic of the quality of tetrahedra in the triangulation of a three-dimensional region. [ABSTRACT FROM AUTHOR]

Single crystals of Ba2YAlO5 and of the α and β phases of Ba6Y2Al4O15 suitable for X‐ray structure analysis were obtained via grain growth of polycrystalline samples prepared by solid‐state reactions. Ba2YAlO5 was found to have a monoclinic crystal structure, with lattice parameters a = 7.2333 (7), b = 6.0254 (5), c = 7.4294 (7) Å and β = 117.249 (3)°, and to belong to the space group P21/m, while α‐Ba6Y2Al4O15 was determined to be monoclinic, with a = 5.9019 (2), b = 7.8744 (3), c = 9.6538 (3) Å and β = 107.7940 (10)°, and the space group Pm, and β‐Ba6Y2Al4O15 was found to be monoclinic, with a = 7.8310 (2), b = 5.8990 (2), c = 18.3344 (6) Å and β = 91.6065 (11)°, and the space group P2/c. In each of these compounds, BO6 octahedra in ABO3 perovskite‐type structures were replaced by AlO4 tetrahedra and YO6 octahedra. Polycrystalline samples in which some Y atoms were replaced with Eu exhibited orange–red luminescence in the range 580–730 nm in response to exposure to radiation having a wavelength of approximately 250 nm. [ABSTRACT FROM AUTHOR]

Quantifying genuine entanglement is a key task in quantum information theory. We study the quantification of genuine multipartite entanglement for four-qubit systems. Based on the concurrence of nine different classes of four-qubit states, with each class being closed under stochastic local operation and classical communication, we construct a concurrence tetrahedron. Proper genuine four-qubit entanglement measure is presented by using the volume of the concurrence tetrahedron. For non genuine entangled pure states, the four-qubit entanglement measure classifies the bi-separable entanglement. We show that the concurrence tetrahedron based measure of genuine four-qubit entanglement is not equivalent to the genuine four-partite entanglement concurrence. We illustrate the advantages of the concurrence tetrahedron by detailed examples. [ABSTRACT FROM AUTHOR]

A novel implicit adaptive FDTD mesh generation method based on tetrahedrons is proposed in this paper. According to the vertex coordinates of tetrahedrons which make up an object, non-uniform grid lines are generated first. These grid lines are constrained by the structure of the object and follow three rules mentioned in the paper. The first rule is to find demarcation points of the object and drop grid lines on these points. The second rule is to make sure all mesh sizes are less than one-tenth of the wavelength by adding more grid lines. The last rule is to densify mesh at the fine structure of the object. Then by comparing the positional relationship between center points of Yee cells and tetrahedrons, the object can be discretized by Yee cells. Finally, numerical examples are given to verify the validity and accuracy of this novel method. [ABSTRACT FROM AUTHOR]

The Wigner derivative is the partial derivative of dihedral angle with respect to opposite edge length in a tetrahedron, all other edge lengths remaining fixed. We compute the inverse Wigner derivative for spherical tetrahedra, namely the partial derivative of edge length with respect to opposite dihedral angle, all other dihedral angles remaining fixed. We show that the inverse Wigner derivative is actually equal to the Wigner derivative. These computations are motivated by the asymptotics of the classical and quantum 6j symbols for SU(2). [ABSTRACT FROM AUTHOR]

Simple Summary: The use of drugs based on nucleic acids is a promising direction in antitumor therapy. Some modified oligonucleotide analogs, such as antisense oligonucleotides, have been developed and used as innovative therapeutic agents in some areas of medicine. Many ways to build DNA nanomaterials with predefined shape and function characteristics have been designed. Thus, molecules of potent antitumor drugs, including doxorubicin, therapeutic oligonucleotides, and complex nanoparticles, have been loaded into or conjugated with DNA-based nanomaterials. It was found that DNA-based nanomaterials can increase the efficiency of drug uptake by cells. In this review, we would like to draw attention to some DNA-based nanomaterials, such as tetrahedrons, origami, DNA nanotubes, and aptamers, that have been used as carriers, drugs or target molecules for anticancer drug delivery. DNA nanotechnology has significantly advanced and might be used in biomedical applications, drug delivery, and cancer treatment during the past few decades. DNA nanomaterials are widely used in biomedical research involving biosensing, bioimaging, and drug delivery since they are remarkably addressable and biocompatible. Gradually, modified nucleic acids have begun to be employed to construct multifunctional DNA nanostructures with a variety of architectural designs. Aptamers are single-stranded nucleic acids (both DNAs and RNAs) capable of self-pairing to acquire secondary structure and of specifically binding with the target. Diagnosis and tumor therapy are prospective fields in which aptamers can be applied. Many DNA nanomaterials with three-dimensional structures have been studied as drug delivery systems for different anticancer medications or gene therapy agents. Different chemical alterations can be employed to construct a wide range of modified DNA nanostructures. Chemically altered DNA-based nanomaterials are useful for drug delivery because of their improved stability and inclusion of functional groups. In this work, the most common oligonucleotide nanomaterials were reviewed as modern drug delivery systems in tumor cells. [ABSTRACT FROM AUTHOR]

Mn(II)-based perovskite materials are being intensively explored for lighting applications; understanding the role of ligands regarding their photobehavior is fundamental for their development. Herein, we report on two Mn (II) bromide perovskites using monovalent (perovskite 1, P1) and bivalent (perovskite 2, P2) alkyl interlayer spacers. The perovskites were characterized with powder X-ray diffraction (PXRD), electron spin paramagnetic resonance (EPR), steady-state, and time-resolved emission spectroscopy. The EPR experiments suggest octahedral coordination in P1 and tetrahedral coordination for P2, while the PXRD results demonstrate the presence of a hydrated phase in P2 when exposed to ambient conditions. P1 exhibits an orange-red emission, while P2 shows a green photoluminescence, as a result of the different types of coordination of Mn(II) ions. Furthermore, the P2 photoluminescence quantum yield (26%) is significantly higher than that of P1 (3.6 %), which we explain in terms of different electron-phonon couplings and Mn-Mn interactions. The encapsulation of both perovskites into a PMMA film largely increases their stability against moisture, being more than 1000 h for P2. Upon increasing the temperature, the emission intensity of both perovskites decreases without a significant shift in the emission spectrum, which is explained in terms of an increase in the electron-phonon interactions. The photoluminescence decays fit two components in the microsecond regime—the shortest lifetime for hydrated phases and the longest one for non-hydrated phases. Our findings provide insights into the effects of linear mono- and bivalent organic interlayer spacer cations on the photophysics of these kinds of Mn (II)-based perovskites. The results will help in better designs of Mn(II)-perovskites, to increase their lighting performance. [ABSTRACT FROM AUTHOR]

Fractal structures with self‐similarity are of fundamental importance in the fields of aesthetic, chemistry and mathematics. Here, by taking advantage of constructs the rational geometry‐directed precursor design, we report the construction of two fascinating Platonic solids, the Sierpiński tetrahedron ST‐T and the Sierpiński octahedron ST‐O, in which each possesses a fractal Sierpiński triangle on their independent faces. These two discrete complexes are formed in near‐quantitative yield from the multi‐component self‐assembly of truncated Sierpiński triangular kernel L1 with tribenzotriquinacene‐based hexatopic and anthracene‐based tetratopic terpyridine ligands (L3 and L4) in the presence of metal ions, respectively. The enhanced stabilities of the 3D discrete structures were investigated by gradient tandem mass spectrometry (gMS2). This work provides new constructs for the imitation of complex virus assemblies and for the molecular encapsulation of giant guest molecules. [ABSTRACT FROM AUTHOR]

Fractal structures with self‐similarity are of fundamental importance in the fields of aesthetic, chemistry and mathematics. Here, by taking advantage of constructs the rational geometry‐directed precursor design, we report the construction of two fascinating Platonic solids, the Sierpiński tetrahedron ST‐T and the Sierpiński octahedron ST‐O, in which each possesses a fractal Sierpiński triangle on their independent faces. These two discrete complexes are formed in near‐quantitative yield from the multi‐component self‐assembly of truncated Sierpiński triangular kernel L1 with tribenzotriquinacene‐based hexatopic and anthracene‐based tetratopic terpyridine ligands (L3 and L4) in the presence of metal ions, respectively. The enhanced stabilities of the 3D discrete structures were investigated by gradient tandem mass spectrometry (gMS2). This work provides new constructs for the imitation of complex virus assemblies and for the molecular encapsulation of giant guest molecules. [ABSTRACT FROM AUTHOR]

Tanabe–Sugano diagram is a successful guideline for the energy levels of 3dn electrons for half a century. However, it is developed only under the regular octahedral crystal field. With the surging research interests in the near‐infra‐red luminescence of 3d block transition‐metal elements, it becomes an urgent demand to know the energy level diagram of Cr4 + and Mn5 + with 3d2 configuration, which are usually embedded in the tetrahedral site due to the smaller ionic size. Although the Tanabe–Sugano diagram of 3d8 configuration in octahedron is usually used as a substitution for that of 3d2 configuration in tetrahedron, the result mismatches with the crystal field strength and emission profile. In this work, irreducible tensor operator method is applied to derive the full analytical expressions of 3d2 energy levels in the tetrahedral crystal field, based on which the Tanabe–Sugano diagram of 3d2 configuration in tetrahedron is built for the first time. Also provided is a set of formulas for fast estimation of Dq/B$Dq/B$ values, which shows consistency between the crystal field strength and the emission profile among Cr4+, Mn5+‐doped luminescent materials. As it is hoped, this work could provide more deep insights into the luminescence of 3d2 elements. [ABSTRACT FROM AUTHOR]

This paper discusses a project for linear algebra instructors interested in a concrete, geometric application of matrix diagonalization. The project provides a theorem concerning a nested sequence of tetrahedrons and scaffolded questions for students to work through a proof. Along the way students learn content from three-dimensional geometry and apply eigenvectors, eigenvalues, and diagonalization to calculate a limit. Other concepts found within the project apply cross products and normal vectors. We describe the project's background, offer comments and variations for the given questions, and supply results from administering it ourselves. [ABSTRACT FROM AUTHOR]

The plasmonic properties of tetrahedral aluminum nanoparticles have been investigated using time‐dependent functional theory (TDDFT) calculations. The excitation energies are calculated for tetrahedral aluminum nanoparticles (Aln, n = 10–120) with different charge states. The BP86/DZ model is used to perform geometric optimization calculations for these clusters. The SAOP/DZ and LB94/DZ levels of theory have been used for the excitation energy calculations of these tetrahedral aluminum clusters. The absorption peaks are red‐shifted upon increasing the size of the aluminum nanoparticles. [ABSTRACT FROM AUTHOR]

The problem consists in bounding the number of tetrahedra that share the same volume V , circumradius R , and face areas A 1 , A 2 , A 3 , A 4. A symbolic computation approach is used to prove that the upper bound of the number of tetrahedra is eight. First, the problem is reduced to a counting root problem using the Cayley-Menger determinant formula for the volume of a simplex and some metric equations of the tetrahedron to construct a system of algebraic equations. Then, an investigation of its real roots is done by analyzing the discriminant sequence and extensive numerical computations. [ABSTRACT FROM AUTHOR]

The goal there was constructed a diagram of the state of the system Fe-Zr-Al-Si by method of thermodynamic diagram. With the help of modeling, it is possible to track the phase structure a complex alloy of ferrum-silicon-zirconium. As a result of the calculations, it was found that the Fe-Zr-Al-Si metal system consists of 12 elementary tetrahedron. The sum of the relative volumes of elementary tetrahedron of the Fe-Zr-Si-Al, system equals one (1,00000), which confirms the correctness of the tetrahedron. The analytical equation of each tetrahedron is obtained. As a result, the alloy with a content of 25 % Zr is modeled by the Si-Fe2Al5-FeSi2-Zr6Si5 tetrahedron. The compositions of the alloy with 35 and 50 % Zr are decomposed in the Si-Fe2Al5-FeSi2 - Zr6Si5 and Zr5Si3-Fe - Fe2Al5-FeSi tetrahedra. [ABSTRACT FROM AUTHOR]

In this paper we present two new designs of spherical flexure joints, which are the compliant equivalent of a traditional ball-and-socket joint. The designs are formed by tetrahedron-shaped elements, each composed of three blade flexures with a trapezoidal shape, that are connected in series without intermediate bodies. This is new with respect to the designs currently found in literature and helps to increase the range of motion. We also present two planar (x - y - θ z) flexure joint designs which were derived as special versions of the spherical designs. In these designs the tetrahedron elements have degenerated to a triangular prisms. For detailed investigation we developed equivalent representations of the tetrahedron and triangular prism elements and proved that three of the four constraint stiffness terms depend solely on the properties of the main blade flexure. Furthermore, we derived equations for these stiffness terms which are compared to finite-element simulations, showing a good correspondence for the prism element with a Normalized Mean Absolute Error (NMAE) of 1.9%. For the tetrahedron element, the equations showed to only capture the qualitative behaviour with a NMAE of 34.9%. Also, we derived an equation for the optimal width of the prism element regarding rotational stiffness. • Two new designs of spherical flexure joints are presented. • These are the high-precision compliant equivalent of ball-and-socket joints. • The designs are formed by new tetrahedron-shaped flexure elements. • These enable a large range of motion without adding intermediate bodies. • Design insights and stiffness equations are provided. [ABSTRACT FROM AUTHOR]

Federico Commandino (1509-1575) was born into an influential family from Urbino, Italy. His family's political connections secured him a position as the private secretary to pope Clement VII in 1534. He dedicated most of his life translating several fundamental works from ancient Greek into Latin, including Archimedes, Ptolemy, Euclid, Aristarchus, Pappus, Apollonius, Eutocius, Heron and Serenus [Rosen, E., Biography in Dictionary of Scientific Biography (New York 1970-1990)]. Most notable is his 1565 work titled De centro gravitatis, where an interesting novel idea is presented and explored. In this work, one particular element from Euclid's Elements is extended to tetrahedra: the center of gravity. In our paper we explore the heritage of his work on tetrahedra and we reflect on the educational value of this cornerstone moment in the history of geometry. [ABSTRACT FROM AUTHOR]

In the discontinuous Galerkin time-domain (DGTD) method, tetrahedral meshes are typically used to discretize the computational domain. However, due to their different topological structures, when tetrahedrons or hexahedrons of the same discrete scale are used to divide the same computational domain, there are more tetrahedral mesh units, resulting in higher temporal and spatial complexity. In this article, a hybrid mesh DGTD algorithm based on virtual elements for tetrahedra and hexahedra is proposed to improve the computational efficiency compared with the traditional DGTD method. The fine-structured computational domain and the outer region are computed using tetrahedral and hexahedral meshes, respectively. During calculation, the numerical flux of each interface element requires data from the other subdomain. In this article, virtual elements are established at each subdomain interface to enable the exchange of field values for ease of processing. Edge assignment or field interpolation is applied to sample points to create corresponding virtual units to calculate fringe fields. Finally, the field value of each virtual element is assigned to the corresponding real element for the numerical flux calculation. Numerical results verify the correctness and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) hollow porous structures have attracted great attention in surface-related fields due to their advantages such as large specific surface area, high gas permeability, and low agglomeration. In this work, Al/Mo co-doped porous Co 3 O 4 hollow tetrahedrons derived from MOFs have been obtained using a simple solvothermal synthetic technique. Various characterizations have been used to analyze the crystalline and electronic structure. The results indicate that Al/Mo ions are successfully doped into the Co 3 O 4 lattice and 0.2 at% Al/Mo co-doped Co 3 O 4 shows the best sensing properties among the other Co 3 O 4 based samples. In particular, 0.2% Al/Mo-Co 3 O 4 exhibits the highest response values of 132–100 ppm TEA at 160 °C, which are 33 times as high as those of undoped Co 3 O 4. Furthermore, 0.2% Al/Mo-Co 3 O 4 also displays rapid response and recovery speed (4 s/36 s), low detection limit (0.5 ppm), good selectivity and long-term stability. The reason of enhanced TEA sensing properties is ascribed to the occurrence of 3D hollow porous structure and coupling effect of Al/Mo co-doping. Thus, 0.2 at% Al/Mo co-doped porous Co 3 O 4 hollow tetrahedrons show promising applications in constructing high-performance chemical sensors for TEA detection. • Al/Mo co-doped porous Co 3 O 4 hollow tetrahedrons derived from MOFs are synthesized by a facile method. • 0.2 at% Al/Mo-Co 3 O 4 exhibits high response values and fast response/recovery speed to TEA. • Enhanced sensing properties is attributed to the formation of hollow porous structure and synthetic effect of Al/Mo co-doping. • This work provides a novel method to modulate the structure of materials for the development of related areas. [ABSTRACT FROM AUTHOR]

Lowering the operating temperature of solid oxide fuel cells (SOFCs) requires high performance oxide ion conductor electrolytes. Recently tetrahedra‐based structures have been attracting considerable attention for oxide ion conductor development, among which the layered tetrahedral network melilite structure appears particularly interesting owing to its remarkable capability to accommodate and transport interstitial oxide ions, compared with isolated tetrahedral anion structures. Stabilization and migration mechanisms of interstitial oxide ions in melilites have been systematically investigated using local structural relaxation from both electrostatic Coulomb interaction and chemical bonding aspects based on atomic and electronic structures respectively using experimental and theoretical approaches. These reveal cationic size and chemical bonding effects on stabilization and migration mechanisms of interstitial oxide ions. Lately, full crystallization from glass, an innovative synthesis method, was employed to produce new metastable melilite oxide ion conductors which are inaccessible using classic solid state reaction owing to cationic size effect. Finally, the thermal and chemical stability at low temperature and the high oxide ion conductivity of the best melilite oxide ion conductors based on LaSrGa3O7 are likely to provide real possibilities of applications of melilite‐type electrolytes in SOFCs and other related devices. [ABSTRACT FROM AUTHOR]

At the end of the year 2018, news of a radical transformation of the International System of Units (SI) spread worldwide. Particular excitement was caused by the abandonment of the 140-year-old prototype of kilogram, the base SI unit of mass, stored under the glass bell in Sèvres near Paris, France, and by the introduction of a new definition of kilogram using the quantum-mechanical Planck constant h. The changes were accepted at the 26th session of the General Conference on Weights and Measures (CGPM) held in Versailles, France, on November 18, 2018, and entered into force on May 20, 2019. In the new definitions the SI units are derived by means of seven natural constants, νCs, c, h, e, kB, NA, and Kcd. The article presents the old and the new definitions of the seven base units of the SI system together with the mathematical expressions obtained by solving algebraic equations implicitly contained in the new definitions. The newly defined set of natural units for the base and derived quantities is discussed. The properties and the history of units kilogram and mole as well as the educational aspects of their interpretation are given special attention. Some selected numerical examples are proposed for use in the high school and university chemistry classes. [ABSTRACT FROM AUTHOR]

A stable and enzyme-free method is described for highly sensitive determination of telomerase activity. It is based on the use of a framework nucleic acid (FNA) nanomachine and doxorubicin-spherical nucleic acid (DSNA) tags. Upon incubation with telomerase, the primer-tetrahedron becomes elongated to form the handed swing arm. The extended swing arm autonomously moves along the predefined track consisting of entropy-tetrahedron by consecutive strand displacement under the aid of fuel-tetrahedron. As a result, many (entropy-tetrahedron)-(fuel-tetrahedron) complexes are assembled for combining the DSNA tags. This results in an amplified electrochemical signal, typically measured at around −0.63 V (Ag/AgCl). The use of an enzyme-free FNA nanomachine and of DSNA tags warrants outstandingly high stability and sensitivity. The method shows a broad dynamic correlation of telomerase activity in cell extracts. The analytical range extends from 10 to 1.0 × 104 HeLa cells mL−1 with a lower detection limit of 2 cells mL−1. The differences in telomerase activity between different cancer cells can be easily evaluated. The method was further verified by quantifying telomerase activity of cancer cells in accumulated normal cells. Therefore, the sensing method has great potential for clinical application. [ABSTRACT FROM AUTHOR]

The authors describe a tetrahedral DNA nanostructure loaded with SYBR Green (SG-TDN) for fluorometric determination of nucleic acids. After intercalating into the TDN, fluorescence of SG is enhanced by 260-fold (exc 480 nm, em 524 nm), and the resulting SG-TDN nanoflare displays >7-fold stronger fluorescence than that of FAM-labeled TDN. The SG-TDNs were coupled to magnetic microparticles and polydopamine nanoparticles to construct multi-functional nanoprobes through sequence hybridization using a toehold strand. The method was applied to detect a stretch of microRNA sequence (20 bp) in buffer and in undiluted serum with excellent selectivity, over a wide linear range and with a low limit of detection (0.2 nM). The probe was also applied for visualization of tumor-related microRNA in living cells via fluorescence imaging. [ABSTRACT FROM AUTHOR]

A finite-strain tetrahedron with continuous stresses is proposed and analyzed. The complete stress tensor is now a nodal tensor degree-of-freedom, in addition to displacement. Specifically, stress conjugate to the relative Green-Lagrange strain is used within the framework of the Hellinger-Reissner variational principle. This is an extension of the Dunham and Pister element to arbitrary constitutive laws and finite strain. To avoid the excessive continuity shortcoming, outer faces can have null stress vectors. The resulting formulation is related to the nonlocal approaches popularized as smoothed finite element formulations. In contrast with smoothed formulations, the interpolation and integration domain is retained. Sparsity is also identical to the classical mixed formulations. When compared with variational multiscale methods, there are no parameters. Very high accuracy is obtained for four-node tetrahedra with incompressibility and bending benchmarks being successfully solved. Although the ad-hoc factor is removed and performance is highly competitive, computational cost is high, as each tetrahedron has 36 degrees-of-freedom. Besides the inf-sup test, four benchmark examples are adopted, with exceptional results in bending and compression with finite strains. • Hellinger-Reissner principle with full stress and displacement as independent unknowns. • Continuous stresses and displacements, which are nodal degrees-of-freedom. • Inf-sup test passed for a block geometry. • Excellent bending behavior. • No instabilities detected in compression or tension. [ABSTRACT FROM AUTHOR]

In Part I of this two-part paper, a Macro-Cosserat Point Element (MCPE) was developed based on a Lagrangian formulation of a ten node macro-tetrahedral element. The MCPE provides ten nodal forces as functions of ten nodal positions, similar to standard finite elements. In previous work, it has been shown that a Eulerian formulation of plasticity can remove unphysical arbitrariness of the reference configuration, an intermediate configuration, total deformation measures and plastic deformation measures that are used in the standard Lagrangian formulation of plasticity. The main objective of this Part II is to develop a Eulerian formulation of the MCPE which is implemented for elastic-viscoplastic response. The resulting MCPE satisfies a nonlinear form of a patch test for plasticity. The examples in Parts I and II of this paper indicate that the MCPE is a robust element that can be used with confidence for modeling general material response. [ABSTRACT FROM AUTHOR]

Tuning the morphology of Ag3PO4 photocatalysts with an elevated concentration of KH2PO4 have been successfully conducted. This photocatalyst was prepared by starting material of AgNO3 and KH2PO4. The KH2PO4 aqueous solution with five concentrations of 0.10 M, 0.15 M, 0.30 M, 0.45 M, and 0.60 M was reacted with AgNO3 aqueous solution. The products were characterized using X-ray Diffraction (XRD), UV-Vis Diffuse Reflectance Spectroscopy (DRS), and Scanning Electron Microscopy (SEM). The concentration of KH2PO4 significantly affected the morphology, size, and crystallinity of catalyst. The morphology of Ag3PO4 may be tuned with the synthesis using an elevated concentration of KH2PO4. The sample with the synthesis using 0.15 M of KH2PO4 exhibited the excellent photocatalytic activity. The high photocatalytic activity was caused by the small size of mixed morphology of sphere and tetrahedron, high crystallinity and defect sites. Copyright © 2019 BCREC Group. All rights reserved. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Two tetrahedrons are formed by the stacking faults around the void under 3D compression, slowing void collapse down. • The void firstly collapses along the principal axes of stress, for both 1D and 3D compressions. • The void size and initial temperature have influence on above features to some extent. Abstract The nanoscale void collapse in single crystal aluminum under 1D and 3D compressions at extremely high strain rate was investigated by molecular dynamics. Our simulations reveal the formation of two intersecting tetrahedrons around the void under 3D compression, rather than the shear dislocation loops under 1D compression. The formed tetrahedrons prevent the continuous growth of the shear dislocation loops, which therefore makes the void collapse slow down. For both 1D and 3D compressions, the void collapse is mainly along the three principal axes of stress, resulting in a four-pointed star cross-section of the void along the {1 0 0} plane. The above features are effected by void size and initial temperature. [ABSTRACT FROM AUTHOR]

Abstract The difference between the (squared) sides of the Grace–Danielsson inequality for tetrahedra will be represented as a sum of two nonnegative terms. This gives another proof of the inequality. Examining the denominator allows us to characterize the infinite triangular prism as a degenerate tetrahedron. We give conditions for equality (for a zero gap) as well, and some examples are included. [ABSTRACT FROM AUTHOR]

Abstract A Macro-Cosserat Point Element (MCPE) has been developed based on a ten node macro-tetrahedral element. The macro-tetrahedral element is divided into eight tetrahedral sub-elements, which are each modeled as a ten node Cosserat Point Element (CPE) with all nodes of the sub-elements being kinematically linked to the ten nodes of the macro-tetrahedral element. The MCPE provides ten nodal forces as functions of ten nodal positions, similar to standard finite elements. The MCPE is proposed as a new candidate for a general purpose, simple, robust element that is versatile in the sense that it can be used to mesh complicated regions and can easily incorporate general constitutive models. Example problems show that the MCPE exhibits enhanced robustness relative to the full integration ten node tetrahedron. The cost for this robustness is moderate loss of accuracy of the MCPE for small deformations of coarsely meshed thin structures. Highlights • A Macro-Cosserat Point Element (MCPE) has been developed based on a ten node macro-tetrahedral element. • Eight tetrahedral sub-elements are linked to the ten nodes of the MCPE. • The MPCE is a general purpose, simple, robust element for nonlinear analysis. • This Part I discusses nonlinear isotropic and orthotropic hyperelastic response. [ABSTRACT FROM AUTHOR]

Bipolar electrochemistry is an unconventional but powerful technique in the fields of materials science and analytical chemistry. We report here the one-step cathodic deposition of Ni x Cu 1– x alloys with a composition gradient and a morphology evolution on a copper substrate, based on an in-plane potential gradient over the interface of a bipolar electrode (BPE) and an electrolytic solution. The alloy gradient was characterized using scanning and transmission electron microscopy techniques. As a result, the deposited alloy layer exhibits a composition gradient from 0 to ca. 89% Ni atoms corresponding to an abundant morphology evolution from pyramids to dendrites and to nano/microballs along the surface of the BPE. Electrochemical screenings were performed for the dissected alloy specimens as the electrocatalyst of hydrogen evolution reaction. The present work shows that bipolar electrochemistry can give access to the fabrication of alloys with abundant architectures as high throughput screening candidates. [ABSTRACT FROM AUTHOR]

Although surface plasmon resonance (SPR) technique and aptamer technology shows great potential in analytical and biological chemistry, direct capture and analysis of small molecules using SPR remains tough. Detection sensitivity of aptasensor and recognition ability of aptamer is limited, because direct immobilization of aptamer causes large steric hindrance and strand entanglement. Herein, we chose a typical small molecule-tetracycline (Mw. 444.4 g/mol) as a model, and combined aptamer technology, DNA nanostructure, and commercial Biacore T200 SPR instrument to develop a straightforward format SPR aptasensor. Anti-tetracycline aptamer (Apt76) was fabricated on the top of a tetrahedron nanostructure to provide a better accessibility to tetracycline than the single-stranded Apt76 (ss-Apt76), and thus to improve sensitivity of the SPR aptasensor. The aptasensor was then validated in real world application for tetracycline screening in multiple honey samples, achieving good recovery rates of 80.20–114.3%, intuitive sensorgrams indicating the binding kinetic properties, and high specificity towards tetracycline. LOD of the tetrahedron-based SPR aptasensor was obtained using the real honey sample and calculated to be 0.0069 μg/kg, which was 10-fold range lower than that of the ss-Apt76-based aptasensor. The proof-of-concept demonstrated that aptamers of small molecules can be oriented immobilized on the SPR surface in a uniform nanoscale distance in both lateral and vertical direction, so as to achieve better conformational folding and better accessibility to small molecules. The concept is promising to be a universal and powerful tool for other ligand immobilization and SPR studies for both real world detection and molecular interaction. [ABSTRACT FROM AUTHOR]

We present a simulation method that can create accurate virtual models of hand with arbitrarily curved surfaces and perform distortion-free MCNPX simulations. Generally, MCNPX simulations of objects with arbitrarily curved surfaces are performed through voxelization. In this study, a polygon model is tetrahedralized by TetGen for the construction of the MCNPX geometry to be distortion-free. Then, dose estimation was successfully performed after converting the virtual model into an MCNPX input. A voxelized model was constructed for comparison purposes. The dose estimation functions of the two models were found to be similar, showing a similar amount of computing time by using the mesh tally option with 2e7 histories. [ABSTRACT FROM AUTHOR]

Aristotelian diagrams are used extensively in contemporary research in artificial intelligence. The present paper investigates the geometric and cognitive differences between two types of Aristotelian diagrams for the Boolean algebra B4. Within the class of 3D visualizations, the main geometric distinction is that between the cube-based diagrams (such as the rhombic dodecahedron) and the tetrahedron-based diagrams. Geometric properties such as collinearity, central symmetry and distance are examined from a cognitive perspective, focusing on diagram design principles such as congruence/isomorphism and apprehension. The cognitive effectiveness of the different visualizations is compared for the representation of implication versus opposition relations, and for subdiagram embeddings. [ABSTRACT FROM AUTHOR]

The SERPENT Monte Carlo code has the unique capability to simulate neutron and gamma transport using a stereolithography (STL) geometry. The STL geometry can model irregular complex geometries often encountered, for example, in research reactors. This geometry type can be used in combination with an unstructured mesh-based interface to couple SERPENT to OpenFOAM for CFD analyses. The STL file format also allows printing the geometry model with 3D printers. This work validates SERPENT simulations based on the STL geometry using the GIACINT critical experimental facility and the YALINA Thermal subcritical experimental facility. The results and performances of SERPENT have been compared with those of the well-known MCNP code. Finally, SERPENT computing time has been significantly reduced by using its mesh adaptive search algorithm, which has been introduced to optimize simulations based on the stereolithography STL geometry, and a hybrid modeling that mixes combinatorial and STL geometries. In this work, the STL geometry model of SERPENT involved the use of multiple software and programming languages, including: CUBIT, PYTHON, C, and MATLAB. [ABSTRACT FROM AUTHOR]

An r -gentiling is a dissection of a shape into r ≥ 2 parts which are all similar to the original shape. An r -reptiling is an r -gentiling of which all parts are mutually congruent. The complete characterization of all reptile tetrahedra has been a long-standing open problem. This note concerns acute tetrahedra in particular. We find that no acute tetrahedron is an r -gentile or r -reptile for any r < 10 . The proof is based on showing that no acute spherical diangle can be dissected into less than ten acute spherical triangles. [ABSTRACT FROM AUTHOR]

Polyhedrons have great potentials in various engineering fields due to their superior capability of folding in 3D to achieve a large volumetric ratio of packaging. However, their practical applications are limited by the lack of effective folding schemes with minimum degrees of freedom. Here in the paper we created a transformation between a tetrahedron and a truncated tetrahedron with one degree of freedom by properly setting a movable joint at each vertex. Two schemes of joint arrangement were proposed, and their kinematic behaviours were respectively studied analytically and numerically, where mobility calculations are both based on the truss transformation. Finally, the transformation process using the first scheme was demonstrated through a cardboard prototype fabricated with the origami technique. [ABSTRACT FROM AUTHOR]

The concepts of area of a triangle and volume of a tetrahedron are interpreted as invariants of basic configurations of points in two and threedimensional spaces and their analogues are found in four-dimensional space. The idea of the invariant of a basic configuration of points is continued for n-dimensional space and a general principle for its development is formulated. Methods of analytical geometry (vector-algebraic modeling, affine co-ordinates, point coordinates, vector co-ordinates) and instruments of linear algebra (determinants) are used. [ABSTRACT FROM AUTHOR]

Two clusters with formula [Ln 4 (μ 4 -O)(HL) 3 (SCN) 4 (H 2 O) 2 ] (Ln = Dy ( 1 ), Er ( 2 )) were assembled by the hydrothermal reaction of Ln(SCN) 3 hydrate and symmetrical amidate H 3 L ligand (2-hydroxy-N-[2-hydroxy-3-[(2-hydroxybenzoyl)amino]propyl]benzamide) in the presence of triethylamine. X-ray crystallographic analysis reveals that 1 and 2 are isostructural and are tetranuclear with a μ 4 -O centred Ln 4 tetrahedron core, in which four crystallographically unequivalent lanthanide ions are all seven-coordinated in distorted capped octahedron geometries. Significantly, both clusters show chirality that is induced by coordination of spirally twisted ligands. The magnetic properties of 1 and 2 have been investigated. Both clusters do not exhibit slow magnetic relaxation that may be ascribed to the effect of the symmetry of ligand field on the oblate Dy 3+ and prolate Er 3+ ions, as well as the regular tetrahedral core. [ABSTRACT FROM AUTHOR]

As a diagnostic biomarker, the detection of circular RNA (circRNA) is vital for the early screening of bladder cancer. Usually, the low abundance of circRNA in clinic samples results in the necessarily complicated extraction before detection. In this work, a tetrahedron supported CRISPR/Cas13a cleavage has been explored for direct electrochemical detection of circRNA in urine from bladder cancer. CRISPR/Cas13a system has been reasonably designed to recognize the characteristic back-splice junction site of circRNA. The activated CRISPR/Cas13a by circRNA can cleave uracil bases composed of DNA tetrahedron immobilized on the surface of gold electrode, resulting in the breakage of DNA tetrahedron and the release of electrochemical active molecule methylene blue. By virtue of highly catalytic efficiency of CRISPR/Cas13a and rigid structure of tetrahedron, the developed electrochemical biosensor can directly detect circRNA in 25 μL urine sample with the lowest detection limit of 0.089 fM and linear detection range from 10 fM to 50 nM in less than 10 min, so as to avoid complicated extraction process and benefit for on-site detection. [ABSTRACT FROM AUTHOR]

The paper describes general relations between areas of sides and sections in some prisms and pyramids. The results are obtained by the use of vector product. [ABSTRACT FROM AUTHOR]

This paper describes a new concept for solar detection sensor implementation in photovoltaic dual-axis sun tracker systems. The sensor uses only three units of identical light-dependent-resistors arranged in a tetrahedron and is able to track the source position of the sun or the strongest intensity of visible light. The prototype has been built and tested, resulting in a wide Field of View (289.4°) and minimum error. When this design is compared to other previous types of sun tracking sensors, it has great advantages in terms of sensor quantity, accuracy, effectiveness, and Field of View. [ABSTRACT FROM AUTHOR]

' $$\ldots $$ nihil omnino in mundo contingint, in quo non maximi minimive ratio quapiam eluceat', translated into ' $$\ldots $$ nothing in all the world will occur in which no maximum or minimum rule is somehow shining forth', used to say L. Euler in 1744. This is confirmed by numerous applications of mathematics in physics, mechanics, economy, etc. In this note, we show that it is also the case for the classical 'centres' of a tetrahedron, more specifically for the so-called Monge point (the substitute of the notion of orthocentre for a tetrahedron). To the best of our knowledge, the characterization of the Monge point of a tetrahedron by optimization, that we are going to present, is new. [ABSTRACT FROM AUTHOR]

We investigate extremal problems for quasirandom hypergraphs. We say that a 3-uniform hypergraph H = ( V , E ) is ( d , η , ) -quasirandom if for any subset X ⊆ V and every set of pairs P ⊆ V × V the number of pairs ( x , ( y , z ) ) ∈ X × P with { x , y , z } being a hyperedge of H is in the interval d | X | | P | ± η | V | 3 . We show that for any ε > 0 there exists η > 0 such that every sufficiently large ( 1 / 2 + ε , η , ) -quasirandom hypergraph contains a tetrahedron, i.e., four vertices spanning all four hyperedges. A known random construction shows that the density 1/2 is best possible. This result is closely related to a question of Erdős, whether every weakly quasirandom 3-uniform hypergraph H with density bigger than 1/2, i.e., every large subset of vertices induces a hypergraph with density bigger than 1/2, contains a tetrahedron. [ABSTRACT FROM AUTHOR]

Saddle-like Ag 3 PO 4 particles of tetrahedron structure were successfully synthesized using a co-precipitation method by mixing H 3 PO 4 ethanol solution and AgNO 3 ethanol aqueous solution, where the percentage of ethanol in AgNO 3 ethanol aqueous solution was varied at 0, 50, 80, 90 and 100% (v/v). The photocatalytic performance of the synthesized samples was evaluated by photodegradation of Rhodamine B (RhB) under blue light irradiation (λ = 455 nm). The results showed that the morphology of the Ag 3 PO 4 particles greatly changed depending on the ethanol content in the reaction solution. Excellent photocatalytic activity was observed at 80% (v/v) of ethanol, where the Ag 3 PO 4 showed saddle-like morphology derived from the tetrahedron structure. [ABSTRACT FROM AUTHOR]

Two approaches to predict the overall elastic properties of solids with regularly and irregularly shaped pores are compared. The first approach involves direct finite element simulations of periodic representative volume elements containing arrangements of pores. A simplified algorithm of collective rearrangement type is developed for generating microstructures with the desired density of randomly distributed pores of regular and irregular shapes. Homogeneity and isotropy (where appropriate) of the microstructures are confirmed by generating two-point statistics functions. The second approach utilizes Mori-Tanaka and Maxwell micromechanical models implemented via the cavity compliance contribution tensor (H-tensor) formalism. The effects of pore shape and matrix Poisson's ratio on compliance contribution parameters of different shapes are discussed. H-tensors of cubical, octahedral and tetrahedral pores for several values of matrix Poisson's ratio are published in explicit form for the first time. Good correspondence between the direct finite element simulations and micromechanical homogenization is observed for randomly oriented and parallel pores of the same shape, as well as mixtures of pores of various shapes up to 0.25 pore volume fractions. [ABSTRACT FROM AUTHOR]

Each Platonic polyhedron P can be folded using a continuous folding process into a face of P so that the resulting shape is flat and multilayered, while two of the faces are rigid during the motion. In previous works, explicit formulas of continuous functions for such motions were given and the same result as above was shown to hold for any tetrahedron. In this paper, we show that a truncated regular tetrahedron can be folded continuously via explicit continuous folding mappings into a flat (folded) state, such that two of the hexagonal faces are rigid. Furthermore, given any general tetrahedron P and any truncated tetrahedron Q of P, we show that if Q contains the largest inscribed sphere of P and satisfies some condition, then Q can be folded continuously into a flat folded state such that two of the hexagonal faces of Q are rigid during the motion. [ABSTRACT FROM AUTHOR]