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This research proposes an analytical solution of the nano-concrete-epoxy interaction area within nano crack region of the reinforced concrete beam by applying Newton's third law in static equilibrium. For deriving the governing equation, the imaginary beam with free ends (no support) is considered within nano crack region. This imaginary beam is acted along the imaginary line of concrete-epoxy interface. Newton's third law is applicable for deriving the governing equation because of assuming the absence of frictional and other external forces. The parametric study is performed for implementing the proposed formula of nano interactive area considering variable nano crack depths and thicknesses. The nano interactive area is increased gradually with the increment of depths and thicknesses based on the parametric study because of linear functionality of interactive area and geometry of nano crack region. The maximum interactive area is found to be 314 nm2 at 0.6 ratio of depths and thicknesses of the nano crack. The incremental differences in interactive area between the crack depth or thickness ratios of 0.1 and 0.6 are found to be 25.4% and 1.6% for variations of the crack depth and thickness ratios, respectively. So, the crack depth shows higher impact on the interaction area compared to the thickness of the crack. However, there is a scope for enhancing this research in future by deriving closed-formed analytical formulations to consider appropriate boundary conditions. [ABSTRACT FROM AUTHOR]

In 1965, fuzzy set theory was born, providing a valuable tool to study phenomena where decision-making based on dichotomy is not a simple task. This work is framed in the ideas of fuzzy analytic geometry; more precisely, this paper is devoted to introducing the idea of a fuzzy tangent line to a fuzzy circle in this geometry. For this purpose, three methods are proposed and studied. Moreover, we provide results that establish the conditions for which the proposed methods define the same fuzzy tangent line. [ABSTRACT FROM AUTHOR]

A polygon can represent the boundary of curved text more compactly than a rectangle. However, predicting reasonable polygon lacks of solutions due to the complex spatial relationships caused by having more vertices. The two main challenges are how to satisfy the constraints between vertices and how to cope with data conflicts caused by inconsistent annotation standards. To address these problems, we propose a divide and conquer methodology, in which a polygon is considered as a set of convex quadrangles. By predicting quadrangles in sequence, the vertices of the polygon are obtained consecutively and constrained by the previous ones. Then, we propose a measure for the overlap between convex quadrangles, with which the IoU between two polygons is calculated densely. Our method is derivable and can be trained end-to-end. Also, the polygon prediction branch that we proposed is universal and transplantable. We select basic architecture as the backbone, and the text/non-text classification branch adopts an online hard example mining strategy. Experiments on curved benchmark datasets, namely Total Text and CTW1500, demonstrate that our approach achieves state-of-the-art accuracy. It also maintains a high level of inferring efficiency. [ABSTRACT FROM AUTHOR]

This article explores the concept of luck and the proportions of infinite sets. The author challenges the idea that luck can be measured proportionally, arguing that it is mathematically incorrect to claim that there are more worlds where a proposition is true than false. The article introduces measure theory, a branch of mathematics that compares the sizes of uncountable sets, and highlights its connection to probability theory. It explains how probability measures can be used to determine the likelihood of certain outcomes, such as the probability of Smith winning or losing. The probabilities presented are based on mathematical calculations and should not be interpreted as subjective judgments. [Extracted from the article]

Monitoring joystick operations in power wheelchairs (PWCs) is promising for investigating user-wheelchair interaction and providing quantitative measures to assess the user's driving performance. In this paper, an add-on measurement system, Power Wheelchair Maneuvering Logger (PWhML), is developed to provide an easy-to-implement and cost-effective solution for monitoring the user's joystick operations in PWCs. The proposed system uses two compact inertial measurement units (IMUs), which are respectively attached to the joystick and wheelchair armrest for movement sensing. A coordinate transformation-based method is proposed to estimate the joystick operating angles using the acceleration data measured by the attached IMUs. The accuracy of the proposed method was thoroughly evaluated under different conditions. The evaluation trials in a stationary PWC reported a mean absolute error (MAE) of 0.59° in the forward/backward direction and 0.64° in the leftward/rightward direction, validating the established geometry model for coordinate transformation. The subsequent driving experiments on outdoor test courses demonstrated the effectiveness and robustness of the proposed method in various terrain conditions (MAE of less than 3°). A clustering analysis based on the t-distributed stochastic neighborhood embedding method correctly categorized different driving activities using the joystick operating angles measured by PWhML. These results indicate that integrating the developed PWhML into PWCs can facilitate a quantitative measurement of the user's driving behavior, providing valuable insights to identify careless operation patterns and help PWC users to improve driving performance. [ABSTRACT FROM AUTHOR]

In their research, the authors actively exploit different branches of geometry. For geometric constructions, computer algebra approaches and systems are used. Currently, we are interested in computer geometry, more specifically, the implementation of computer graphics. The use of the projective space and homogeneous coordinates has actually become a standard in modern computer graphics. In other words, the problem is reduced to the application of analytic projective geometry. The authors failed to find a computer algebra system that could implement projective geometry in its entirety. Therefore, it was decided to partially implement computer algebra for visualization of algebraic relations. For this purpose, the Asymptote system was employed. [ABSTRACT FROM AUTHOR]

Water jets impacting the rock cause water hammer effects, resulting in significant damage to the rock. The self-rotating cascade jet breaks rocks through rotational impact, but its water hammer characteristics are still uncertain. The models for water hammer pressure and its duration and dimensionless action length of a cascade jet were constructed using dynamic elasticity and analytic geometry. Moreover, rock-breaking experiments were conducted using a developed cascade nozzle bit to validate the models. The results show that the impact of self-rotating cascade jets on the rock does not generate continuous water hammer pressure. The water hammer characteristics and rock-breaking capacity of the designed jets are ranked as follows: the central jet is the strongest, the first cascade jet is the second strongest, and the second cascade jet is the weakest. The characteristics of the water hammer and rock-breaking capacity for the self-rotating cascade jet increase as the rotational speed and the eccentric distance decrease, the pressure, the impact angle, and the radius increase. The results can lay a theoretical foundation for understanding the rock-breaking mechanism of the self-rotating cascade jet and developing new types of pulsed jets. Highlights: Water hammer models were developed and validated for a self-rotating cascade jet impinging on a rock. The water hammer pressure of a self-rotating cascade jet impinging on the rock was not sustained. The influence of jet property parameters on the water hammer characteristics was demonstrated. [ABSTRACT FROM AUTHOR]

A Ni(II) complex of 3,3′-(-(pentane-3,3-diylbis(1H-pyrrole-5,2-diyl))bis(diazene-2,1-diyl)) dipyridine, NiL, has been synthesized and characterized. In the crystal, the Ni(II) ion is in square-planar geometry by coordinating to two pyrrole nitrogen atoms and two azo nitrogen atoms. Anagostic C–H···Ni interactions, as well as C–H···N hydrogen bond were found play important role in the self-assembly of the complex molecules. The intermolecular interactions were evaluated by Hirshfeld surface analysis. Frontier molecular orbitals (HOMO and LUMO), their energy gap and associated reactive parameters were calculated to understand the properties of the complex. UV–Vis spectrum of the complex were also performed. Anagostic C–H···Ni interactions were found play important role in the crystal of the Ni(II) complex with 3,3'-(-(pentane-3,3-diylbis(1H-pyrrole-5,2-diyl))bis(diazene-2,1-diyl)) dipyridine. [ABSTRACT FROM AUTHOR]

For several decades, cooperative control of autonomous mobile robots has been an active research area with potential applications in dynamic areas such as agriculture, industrial plants, and the military. Although numerous research studies on pattern formation using multiple mobile agents have been conducted, no algorithm for symmetric pattern formation that is independent of the number of agents and prioritizes user control has been introduced. This article demonstrates an attempt to manifest an end-to-end symmetrical pattern in a swarm of mobile robots. Here, a two-staged paradigm named SymSwarm is developed, which incorporates the novelty of forming symmetrical formations around a point within a coveted area via decentralized communication among the swarm. SymSwarm is built on a novel concept of a bio-inspired state model called compete and point state model (CPSM), which enables smarter and more robust computation and self-regulation. While most bio-inspired models focus on the characteristics of bees, ants, cats, chimpanzees, and a variety of other animals, this paradigm focuses on the competitive sentiment and leadership ability of human beings to shape the CPSM mentioned above. The algorithm for acquiring symmetrical points is developed using the circle polygon analogy in Cartesian geometry. The following sections propose a decentralized communication mechanism for adjacent consecutive robots as well as a heuristic nearest point finder algorithm. The proposed paradigm is evaluated using robotics simulator (V-REP), and the results indicate that it is consistently successful and has a low rate of pattern formation error in the presence or absence of obstacles in the environment. [ABSTRACT FROM AUTHOR]

In this paper, the aim is to make a theoretical contribution by focusing on the origin, characteristics, and potential values of the concepts of instrumental and relational understanding. Five characteristics are identified to make it easier to operationalise the concepts and use them as an analytical framework. There is also a focus on how the concepts are closely related to two rationales for learning, the instrumental and the social rationale. The potential values of the concepts and their rationales are shown by using them to suggest a revision of the van Hiele framework and to analyse three empirical examples concerning young students' understanding of triangles and a cylinder. [ABSTRACT FROM AUTHOR]

A hydrazone ligand, 4-chlorobenzaldehyde hydralazine hydrazone (LH), has been synthesized. Our initial attempts to synthesize Co+2, Ni+2, Cu+2 and Zn+2 metal complexes of LH resulted in a cyclized triazole product (T). Structure of both the LH and T is characterized by single-crystal X-ray diffraction pattern analysis. Synthesis of desired metal complexes is achieved by using LH in its monohydrochloride salt form (LH.HCl), thus preventing cyclization of LH to T. Mass, IR, NMR, UV–Vis spectroscopic techniques, thermal and other physicochemical methods were used for the structural elucidation of the metal complexes. On the basis of electronic and magnetic properties of the complexes, four coordinate square-planar geometry for Ni+2 complex, while Td geometry for Cu+2 and Zn+2 complex was assigned. Around Co (II) ions, Oh geometry was assigned. In vivo antihypertensive assay of the synthesized compounds is carried out in rats with fructose-induced hypertension to measure the blood pressure and tail pulse. Copper complex and the LH have exhibited antihypertensive activity at par with the well-known antihypertensive drug hydralazine. [ABSTRACT FROM AUTHOR]

This can be extended to the I n i th root HT ht by an I n i -polar generalization of the Cassini ovals with equation HT ht , employing the I n i th roots of unity as poles [[8]]. We assume HT ht and HT ht , as in the first row of Table 2, so that HT ht . Hence, HT ht is parallel to - or offset from - I W i at distance HT ht . [Extracted from the article]

The existing comparative studies of intact rock failure criteria do not typically consider the tensile stress zone and failure angle prediction. A new comparative study of nine intact rock strength criteria worth to list them here was performed under the framework of analytical geometry, with respect to their geometric characteristics in different cutting planes of the failure envelopes in three-dimensional space as well as predictive capacities for strength and failure angle. For this purpose, a universal failure angle formula was derived as a guideline to deduce the specific expression for each criterion. The σ1–σ3 cutting plane displays two categories of the intact rock failure criteria: overlapping and separate compressive and tensile meridian boundaries. Experimental strength data and failure angle observation of two sandstones under complex compressive stress conditions highlight the failure criteria of Mogi-1967, Mogi-1971, nonlinear unified and Hoek–Brown in terms of strength and failure angle prediction. It is probably the first of its kind to date to evaluate different intact rock failure criteria by relating the failure angle and strength. This innovative comparative work enlightens the future advancement of the intact rock failure criterion with the consideration of the tensile stress zone and failure angle observation. Highlights: Analytical geometric technique revealed the existing intact rock failure criteria were inadequate to reflect the tensile behaviors or failure angle. A universal failure angle formula was derived for any failure function through stress transformation. An innovative procedure relating the failure angle and strength predictions was proposed and used to evaluate nine intact rock failure criteria. [ABSTRACT FROM AUTHOR]

The thin-walled workpiece is affected by the weak rigidity of the workpiece which will lead to force-induced deformation during the five-axis flank milling. To solve this problem, this paper explores the relationship between cutting force and deformation after establishing the cutting force model. Firstly, the error function under single tool position is established to optimize the tool axis vector, so that the tool can close to the ruled surface, and then tool position is extracted to represent the tool posture in the five-axis flank milling process. Based on the geometric model, a calculation model of cutter-workpiece engagement (CWE) is described by combining the discrete geometry method and the analytical method. And the problem of calculating the instantaneous chip undeformed thickness (ICUT) is transformed into the intersection problem of cylinder surface from cutting point to previous tooths; the model is used to simulate the five-axis milling process and predict the cutting force. On the basis of the above work, the force-induced deformation model of tool and workpiece is established to compensate the deviation by adjusting the tool point and tool axis vector. The effectiveness of force model is verified by cutting force experiments. After that, the machining experiments were carried out by the optimized tool paths, and the measurement results show that the optimized machining error is obviously improved. [ABSTRACT FROM AUTHOR]

Its base has length HT ht . By similar triangles, HT ht . The images of segments orthogonal to the major axis, like HT ht and HT ht , do not change length. In Figure 5, left, HT ht is the polar of the point at infinity on HT ht , and vice versa. [Extracted from the article]

Geometric algebra is based on the works by Grassmann and Clifford. Its main objects of research are polyvectors (p-vectors) and multivectors. Polyvectors, together with the exterior product, implement the Grassmann algebra, while multivectors with the geometric product implement the Clifford algebra. Multivector algebra generalizes many operations and objects of analytic geometry and differential geometry (e.g., vector and mixed products, normal vectors and binormals, etc.) to the multidimensional case, as well as provides their geometric interpretation. Complex numbers and quaternions are isomorphic to multivectors of a special kind. This paper applies certain ideas of geometric algebra to solve problems that occur in computer geometry. For this purpose, the Grassmann.jl package for Julia is used. [ABSTRACT FROM AUTHOR]

Cholera toxin (CT) and Escherichia coli heat-labile enterotoxin (LT) are structurally similar AB5-type protein toxins. They move from the cell surface to the endoplasmic reticulum where the A1 catalytic subunit is separated from its holotoxin by protein disulfide isomerase (PDI), thus allowing the dissociated A1 subunit to enter the cytosol for a toxic effect. Despite similar mechanisms of toxicity, CT is more potent than LT. The difference has been attributed to a more stable domain assembly for CT as compared to LT, but this explanation has not been directly tested and is arguable as toxin disassembly is an indispensable step in the cellular action of these toxins. We show here that PDI disassembles CT more efficiently than LT, which provides a possible explanation for the greater potency of the former toxin. Furthermore, direct examination of CT and LT domain assemblies found no difference in toxin stability. Using novel analytic geometry approaches, we provide a detailed characterization of the positioning of the A subunit with respect to the B pentamer and demonstrate significant differences in the interdomain architecture of CT and LT. Protein docking analysis further suggests that these global structural differences result in distinct modes of PDI-toxin interactions. Our results highlight previously overlooked structural differences between CT and LT that provide a new model for the PDI-assisted disassembly and differential potency of these toxins. [ABSTRACT FROM AUTHOR]

Four-dimensional cosmological models are studied on a boundary of a five-dimensional Anti-de Sitter (AdS5) black hole with AdS Reissner-Nordström and scalar charged Reissner-Nordström black hole solutions, where we call the former a "Hairless" black hole and the latter a "Hairy" black hole. To obtain the Friedmann-Robertson-Walker (FRW) spacetime metric on the boundary of the AdS5 black hole, we employ Eddington-Finkelstein (EF) coordinates to the bulk geometry. We then derive modified Friedmann equations on a boundary of the AdS5 black hole via AdS/CFT correspondence and discuss its cosmological implications. The late-time acceleration of the universe is investigated in our models. The contributions coming from the bulk side is treated as dark energy source, and we perform MCMC analyses using observational data. Compared to the ΛCDM model, our models contain additional free parameters; therefore, to make a fair comparison, we use the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) to analyze our results. Our numerical analyses show that our models can explain the observational data as reliable as the ΛCDM model does for the current data. [ABSTRACT FROM AUTHOR]

We study the membrane wrapping mode corrections to the Kaluza-Klein (KK) 6-brane in eleven dimensions. We examine the localized KK6-brane in the extended space in E7(7) exceptional field theory. In order to discuss the physical origin of the localization in the extended space, we consider a probe M2-brane in eleven dimensions. We show that a three-dimensional N = 4 gauge theory is naturally interpreted as a membrane generalization of the two-dimensional N = (4, 4) gauged linear sigma model for the fundamental string. We point out that the vector field in the N = 4 model is identified as a dual coordinate of the KK6-brane geometry. We find that the BPS vortex in the gauge theory gives rise to the violation of the isometry along the dual direction. We then show that the vortex corrections are regarded as an instanton effect in M-theory induced by the probe M2-brane wrapping around the M-circle. [ABSTRACT FROM AUTHOR]

Knowledge about protein structure assignment enriches the structural and functional understanding of proteins. Accurate and reliable structure assignment data is crucial for secondary structure prediction systems. Since the 1980s, various methods based on hydrogen bond analysis and atomic coordinate geometry, followed by machine learning, have been employed in protein structure assignment. However, the assignment process becomes challenging when missing atoms are present in the protein files. Our method proposed a multi-class classifier program named DLFSA for assigning protein secondary structure elements (SSE) using convolutional neural networks (CNNs). A fast and efficient GPU-based parallel procedure extracts fragments from protein files. The model implemented in this work is trained with a subset of the protein fragments and achieves 88.1% and 82.5% train and test accuracy, respectively. The model uses only Cα coordinates for secondary structure assignments. The model has been successfully tested on a few full-length proteins also. Results from the fragment-based studies demonstrate the feasibility of applying deep learning solutions for structure assignment problems. [ABSTRACT FROM AUTHOR]

Optimal design parameter combination and transmission optimization for plane-generated enveloping toroid hourglass worm drive are proposed. The modeling frame and mathematical model of the worm were constructed first to provide a perfect transmission. Then, the mathematical representations of transmission performance, including lubrication angle, induced normal curvature, and length of meshing line for worm drive, were derived according to differential geometry and coordinate transformation approach. In addition, the influence of various design parameters on transmission performance was associated with main parameters, and the influence of the main parameters on transmission was evaluated. Next, a multivariate transmission optimization considering lubrication effect, bearing capacity and contact strength was conducted in view of the whole meshing cycle. The optimal global solution of the multivariate optimization model was also evaluated using a genetic algorithm. Calculation and experimental results indicated the optimization study was in good agreement with experimental results. Finally, the comprehensive transmission performance of the worm drive has an increase of 9.2 %. [ABSTRACT FROM AUTHOR]

A fiber-optic shape sensing based on 7-core fiber Bragg gratings (FBGs) is proposed and experimentally demonstrated. The investigations are presented for two-dimensional and three-dimensional shape reconstruction by distinguishing bending and twisting of 7-core optical fiber with FBGs. The curvature and bending orientation can be calculated by acquiring FBG wavelengths from any two side cores among the six outer cores. And the shape sensing in three-dimensional (3D) space is computed by analytic geometry theory. The experiments corresponding of two-dimensional (2D) and 3D shape sensing are demonstrated and conducted to verify the theoretical principles. The resolution of curvature is about 0.1m−1 for 2D measuring. The error of angle in shape reconstruction is about 1.89° for 3D measuring. The proposed sensing technique based on 7-core FBGs is promising of high feasibility, stability, and repeatability, especially for the distinguishing ability on the bending orientation due to the six symmetrical cores on the cross-section. [ABSTRACT FROM AUTHOR]

The reference pulse system avoids most of the constraints introduced by the sampled-data system. The bottleneck of the reference pulse system is the non-constant feedrate of the incremental step IPOs. The wrong initialized software DDA-IPOs make these IPOs unusable. The three conditions to apply the reference pulse system are the small incremental step, the small execution time per step, and the constant speed along the curve. Cascading an ultra-fast 3-lines algorithm "PRM-cs" to the current reference pulse IPO quickly converts this IPO to a constant speed reference pulse IPO. This applies to 2D-lines, 3D-lines, 2D-curves, and 2D-NURBS. The PRM-cs measures, in real time, the length of the discrete curve and the PRM-cs is completely new. The 2D-IPOs are perfect or nearly-perfect, but the current 3D-lines are mostly imperfect, meaning that the accuracy is much less (e.g., 37% worse) than the accuracy of the perfect or best 3D-line IPOs. The accuracy of the imperfect 3D-lines is also bounded; therefore, they can be used as constant speed 3D-line IPOs when the production manager agrees. The global definition (given by the Digital Analytic Geometry) of a discrete 3D-line is imperfect, too. The three causes of the imperfect 3D-lines will be given. All lines and curves have major axis segments. The major axis principle holds for the actual 3D-line IPOs but that is generally wrong. All existing pulse-rate or PRM-IPOs use a wrong initialization, which deteriorates the accuracy, but the new PRM-cs and the updated PRM-IPO use the right initialization. The new constant speed listSIM-IPO can be used in real time for every 2D and 3D-curve and it can be used as a benchmark for every IPO. The third-degree Trident NURBS shows that the constant speed MIDP-IPO is flexible, that it can be used for NURBS, that it can be used for conics, and that it calculates the gradient (direction vector) in real time. The paper shows that the reference pulse method is much better than the existing sampled-data methods. [ABSTRACT FROM AUTHOR]

We show that there is a unique hypersurface of minimal degree passing through the non-faces of a polytope which is defined by a simple hyperplane arrangement. This generalizes the construction of the adjoint curve of a polygon by Wachspress (A rational finite element basis, Academic Press, New York, 1975). The defining polynomial of our adjoint hypersurface is the adjoint polynomial introduced by Warren (Adv Comput Math 6:97–108, 1996). This is a key ingredient for the definition of Wachspress coordinates, which are barycentric coordinates on an arbitrary convex polytope. The adjoint polynomial also appears both in algebraic statistics, when studying the moments of uniform probability distributions on polytopes, and in intersection theory, when computing Segre classes of monomial schemes. We describe the Wachspress map, the rational map defined by the Wachspress coordinates, and the Wachspress variety, the image of this map. The inverse of the Wachspress map is the projection from the linear span of the image of the adjoint hypersurface. To relate adjoints of polytopes to classical adjoints of divisors in algebraic geometry, we study irreducible hypersurfaces that have the same degree and multiplicity along the non-faces of a polytope as its defining hyperplane arrangement. We list all finitely many combinatorial types of polytopes in dimensions two and three for which such irreducible hypersurfaces exist. In the case of polygons, the general such curves are elliptic. In the three-dimensional case, the general such surfaces are either K3 or elliptic. [ABSTRACT FROM AUTHOR]

The graph G ′ obtained from a graph G by identifying two nonadjacent vertices in G having at least one common neighbor is called a 1-fold of G. A sequence G 0 , G 1 , G 2 , ... , G k of graphs such that G 0 = G and G i is a 1-fold of G i - 1 for each i = 1 , 2 , ... , k is called a uniform k-folding of G if the graphs in the sequence are all singular or all nonsingular. The fold thickness of G is the largest k for which there is a uniform k-folding of G. We show here that the fold thickness of a singular bipartite graph of order n is n - 3 . Furthermore, the fold thickness of a nonsingular bipartite graph is 0, i.e., every 1-fold of a nonsingular bipartite graph is singular. We also determine the fold thickness of some well-known families of graphs such as cycles, fans and some wheels. Moreover, we investigate the fold thickness of graphs obtained by performing operations on these families of graphs. Specifically, we determine the fold thickness of graphs obtained from the cartesian product of two graphs and the fold thickness of a disconnected graph whose components are all isomorphic. [ABSTRACT FROM AUTHOR]

With the distinguished wavefront characteristics of vortex electromagnetic wave carrying orbital angular momentum (OAM), the OAM beams have been exploited for radar imaging in recent years. In this paper, the computational imaging model is built using OAM wave, which enables the target reconstruction with limited measurements. The measurement matrix is designed, and the target reconstruction method is proposed in the Cartesian coordinate. Simulation results indicate that the proposed computational imaging approach is robust against noise influence. Furthermore, the outdoor experiments are carried out, for the first time, to validate the super-resolution imaging ability of this novel technique. Experimental results show good agreement with theoretical analyses. This work can advance the development of OAM-based sensing technology. [ABSTRACT FROM AUTHOR]

The gravitational shift of electromagnetic frequency in the strong field limit is usually investigated under the common scenario, where the light receiver is far away from the central body while the emitter is in the strong-field region of the lens. In this paper, the gravitational frequency shift of light caused by a Reissner–Nordström (RN) black hole is studied numerically in the traditional strong-field scenario, as well as in the scenario where both the light emission and reception events happen in the strong-field region of the black hole. In order to obtain the numerical results of the gravitational redshift, we first derive the exact null equations of motion in the RN geometry in harmonic coordinates. For a given light observer, a new numerical technique is proposed in the integration of the geodesic equations to determine the spatial position of the emitter, considering the fact that their spatial positions are not always known simultaneously. Our work might be helpful to the related observations for probing strong gravity. [ABSTRACT FROM AUTHOR]

We explicitly determine all the relative generalized Hamming weights of affine Cartesian codes using the notion of footprints and results from extremal combinatorics. This generalizes the previous works on the determination of relative generalized Hamming weights of Reed–Muller codes by Geil and Martin, as well as the determination of all the generalized Hamming weights of the affine Cartesian codes by Beelen and Datta. [ABSTRACT FROM AUTHOR]

These particular discs were introduced by Lempert in [[43]] in his study of the complex geometry of bounded smooth strongly convex domains in HT ht . In the remainder O(3), I z i is of weight one and HT ht of weight two. Remark 3.11 The Banach space I X i should be thought as the set of allowable perturbation I M i of HT ht . Recall also that the norm on HT ht has been defined in (3.8). [Extracted from the article]

Mass-spring systems (MSS) simulating elastic materials obey constraints known in elasticity as the Cauchy relations, restricting the Poisson ratio of isotropic systems to be exactly ν = 1 / 4 . We remind that this limitation is intrinsic to centrosymmetric spring systems (where each node is a center of symmetry), forbidding them for instance to simulate incompressible materials (with ν = 1 / 2 ). To overcome this restriction, we propose to supplement the spring deformation energy with an energy depending on the volume only, insensitive to change of shape, permitting MSS to simulate any real isotropic materials. In addition, the freedom in choosing the spring constants realizing a given elastic behavior allows to manage instabilities. The proposed hybrid model is evaluated by comparing its response to various deformation geometries with analytical model and/or finite element model. The results show that the hybrid MSS model allows to simulate any compressible isotropic elastic material and in particular the nearly incompressible (Poisson ratio ν ≃ 1 / 2 ) biological soft tissues to which it is dedicated. [ABSTRACT FROM AUTHOR]

The usual conception of the philosophy of mathematics is based on the mid-twentieth century configuration of the discipline, giving pre-eminence in an almost exclusive way to the abstract, pure mathematics of set-theoretic structures. The mid-twentieth century obsession with purity seems now gone, and there is much philosophical interest in the project to contribute to a broader view of maths that underlines the close relation - both historically and systematically, from today's point of view - of "mathematics" and "physics". 20132: London; Routledge 4 Epple M, Kjeldsen TH, Siegmund-Schultze R. From "mixed" to "applied" mathematics: Tracing an important dimension of mathematics and its history. [Extracted from the article]

One of the major limitations of micro-milling applications in industries is its fast tool wear, which leads to low machining precision and efficiency. An accurate force model is fundamental for optimization micro-milling processes and minimize the tool wear. However, a generic model with tool runout and wear effect has not yet been established, which limits its practical application under varied working conditions. In this paper, a new idea is introduced by applying the spatial analytic geometry (SAG) method, under this framework the micro-milling force model is established based on the analysis of the geometrical relationship among the cutting edge positions, pre-processed workpiece morphology, and cutting force directions considering tool runout and wear effect. In this model, the tool runout is identified exclusively by only one parameter, namely the distance away from the center that perpendicular to the feed direction, so that it could be calibrated conveniently by calculating the ratio of resultant forces corresponding to different cutting edges. The tool wear–induced force is then modeled as increment of force coefficients to the original model. Therefore, the new force model with considering tool wear has the same form as the fresh tool. Finally, the accuracy and efficiency of the model are validated by experiments under varied working conditions. [ABSTRACT FROM AUTHOR]

The geometrical error of the formed part is one of the most significant limitations that restricts the widespread application of incremental sheet forming (ISF) in aerospace industry. The geometry of ISF parts is dependent upon the tool path, so its correction can improve the part precision. Previous research has utilized model predictive control approach to achieve this, but the method was restricted to simple convex shapes. In this study, the tool path and the formed shape were parameterized and the analytical models of geometry responses relative to tool perturbations were proposed. Then, a model predictive control algorithm was developed, aiming at reducing the geometrical errors of the parts with complex non-convex shapes in the ISF process. Experimental validation of the developed control algorithm was carried out by forming a complex shape by single-point incremental forming. The results show that the developed control algorithm greatly reduced the geometrical error in the closed-loop process. [ABSTRACT FROM AUTHOR]

The evolution of the magnetic configuration in the solar corona is studied. The curvature of the K-corona helmets obtained from an analytical approximation of the geometry of the helmet axis was used as an indicator of the configuration change. The period of minimum solar activity was analyzed with solar eclipse materials. As a result of the analysis, the dependence of the curvature value on the latitude of the position of the helmet base and the phase of the solar cycle has been obtained. It has been established that this dependence is different for the period of solar-activity growth (the beginning of the cycle) and its decline. It was found that there is a sharp decrease in the curvature to almost zero at the beginning of the solar cycle. During the decline of the 23rd cycle and at the beginning of the 24th cycle, the change of the curvature of the helmets differs from the trend of the previous solar cycles. The apparent reason for this is a change in the conditions of the generation of the solar magnetic field. The found latitudinal–phase dependences of the curvature of the coronal helmets indicate a difference in the coronal magnetic configuration during periods of decline and increase in solar activity, as well as a sharp reorganization of the configuration at the beginning of the new solar cycle. [ABSTRACT FROM AUTHOR]

Two types of functional monomers, 3-(2-aminoethylamino)-propyl-trimethoxysilane (AAPTS) and 3-aminopropyl-triethoxysilane (APTES), with similar amino groups but different denticity (AAPTS: bi-dentate; APTES: mono-dentate) were used to prepare Cu-ion-imprinted hybrids (IIHs), and their influences on the imprinting quality, adsorption ability, and selectivity of the IIHs were symmetrically investigated. The AAPTS-IIHs exhibited the highest imprinting factor (IF) of 17.7 at the Cu/AAPTS = 1/1 and the highest Cu selectivity (k > 6.5) at the Cu/AAPTS = 0.5–1/1, whereas the two corresponding performances (IF = 22.6, k > 1.7) in the APTES-IIHs occurred at the Cu/APTES molar ratio of 0.124/1 and 0.5/1, respectively. Stronger complexation ability of the bidentate ligand led the AAPTS-IIH to exhibit 6.3–6.9 times higher Cu affinity than the APTES-IIH powder. In addition, it resulted in a higher degree of homogeneity among the binding sites and created more selective environment within the imprinted cavities than the mono-dentate APTES monomer did. Square-planar 4-coordinate and linear 2-coordinate Cu complexes were the major forms imprinted in the AAPTS-based and the APTES-based systems, respectively. The exclusion ability of the AAPTS-IIH for the reference ions was in the order of Pb2+~Zn2+ > Ni2+ > Hg2+, while it was Zn2+> Pb2+> Ni2+> Hg2+ in the APTES-IIH powder. The imprinted hybrids select ions mainly based on the coordinate geometries of the ion-complexes, and the complexation stability was the second priority. [ABSTRACT FROM AUTHOR]

Harriot had the ingenious idea of first setting the polynomial equal to zero, thereby setting up an equation, a polynomial equation, and asking for the numbers that satisfy the equation, something we now do naturally. However, Harriot did not know of Fermat's principle, since Pierre de Fermat had not yet been born when Harriot was performing his light experiments in 1597. Arianrhod tells us that many scientists before Harriot carried out similar experiments and came upon inaccurate or invalid results. Five years after his correspondence with Harriot, he wrote an essay, I The Six-Cornered Snowflake i , on why snowflakes always have sixfold symmetry, which includes Harriot's principle of the best way to stack cannonballs on ships.[2] For the next 410 years it was known as Kepler's conjecture. [Extracted from the article]

An exponential curve is the graph of an exponential function HT ht . Let us choose a length unit such that HT ht and a time unit such that the velocity of the horizontal translation is 1. I The point i I D i I traces a tractrix if and only if i HT ht . I The point i I B i I traces an exponential curve if and only if i HT ht. [Extracted from the article]

In drilling engineering, it is extremely challenging to drill a prescribed wellbore over several thousand meters. One of the main difficulties arises from accurately predicting and controlling the directional drilling performance, caused by the complex nonlinear dynamics of the slender drilling assembly and its interactions with the surrounding rocks. Nowadays, the simplified analytical geometry method, which has been adopted as the industry standard, can merely offer a rough estimation of the drilling direction, while the high-accuracy finite element method is computationally inefficient. This study is intended to provide a straightforward prediction of the drilling direction for a long drilling distance accurately and efficiently by proposing a dynamical simulation method based on the flexible multibody approach. Three techniques were adopted to achieve the critical objective of the paper. First, an Arbitrary Lagrangian–Eulerian formulation was used to provide a new approach to balance the efficiency and accuracy. Additionally, it can perfectly simulate the realistic drilling operation that drill pipes are continuously added to the drill string one by one through dynamically inserting new beam elements into the existing model. Second, the whole drill string and its interaction with the wellbore were all considered to carry out a high-fidelity simulation. Finally, the bit–rock interaction model was introduced to offer a straightforward way of evaluating the steerability of drilling assemblies. The presented method and model were validated by the consistency between the simulated wellbore trajectory and the in-field experimental data and are ready to be applied in drilling tools design, real-time drilling simulation, and drilling direction control. [ABSTRACT FROM AUTHOR]

This paper reported an analytical formulation for the optimum geometry of a uniform pressure coil used in electromagnetic forming and welding. To characterize the energy efficiency of the coil, we defined the objective function as the ratio between the produced magnetic pressure and the required magnetic energy. We then deduced an analytical formulation of the objective function in terms of the geometry and electromagnetic parameters. Based on the analytical formulation, we finally deduced the optimum configuration of the coil geometry in analytical form. To validate the proposed analytical formulation, we analytically and numerically analyzed a uniform pressure coil fabricated in our laboratory, showing that the proposed analytical formulation can well reproduce the numerical results over a broad range of geometric parameters. In addition, it was found that the uniform pressure coil exhibits an optimum channel height, which can be analytically expressed in terms of the coil geometry. In summary, the present study provides an efficient method for designing a uniform pressure coil. [ABSTRACT FROM AUTHOR]

Expansion of measured dynamic response at a limited set of points is of great interest in the study of structural dynamic systems. Measurements at limited points on a structure can be expanded to unmeasured points by using System Equivalent Reduction Expansion Process (SEREP). However, a finite element model is required to obtain the mode shapes of the system. In this work, a non-model based expansion technique is proposed to expand the vibration characteristics at a sparse set of points to a much larger set of points without the use of a finite element model. Shape functions based on orthogonal polynomials can be used to decompose the deformation of vibrating structures into the summation of a set of shape functions with corresponding weighting coefficients. To obtain the vibration characteristics at an augmented set of points, measurements at a sparse set of points can be related to a set of shape functions which have the same mesh resolution as the sparse configuration. The vibration characteristics at an augmented set of points can then be reconstructed from the shape functions of the high resolution and scaled shape function weighting coefficients of the sparse configuration. Only a sparse set of measurements, geometry and coordinates of measured points are needed. In the work studied here, an analytical plate and a Base-Upright (BU) structure are used as samples to study the application of the proposed method. Both analysis and experiment are used to prove the concept. [ABSTRACT FROM AUTHOR]

The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the longitudinal and transverse fields satisfy scalar Helmholtz equations that can be solved using a desingularized boundary element method (BEM) framework. The curl free longitudinal and divergence free transversal conditions can also be cast as additional scalar Helmholtz equations. When compared to other BEM implementations, the current framework leads to smaller matrix dimensions and a simpler conceptual approach. The numerical implementation of this approach is benchmarked against the 3D elastic wave field generated by a rigid vibrating sphere embedded in an infinite linear elastic medium for which the analytical solution has been derived. Examples of focused 3D elastic waves generated by a vibrating bowl-shaped rigid object with convex and concave surfaces are also considered. In the static zero frequency limit, the Helmholtz decomposition becomes non-unique, and both the longitudinal and transverse components contain divergent terms that are proportional to the inverse square of the frequency. However, these divergences are equal and opposite so that their sum, that is the displacement field that reflects the physics of the problem, remains finite in the zero frequency limit. [ABSTRACT FROM AUTHOR]

We employ 2D Cartesian geometry model of thermochemical convection with non-Newtonian rheology and phase transitions, in the presence of floating deformable continents. Using a mantle model with continental crust, lithosphere and the material of the oceanic crust that can be subjected to eclogitization we study the stages of supercontinent cycle: assembly, evolution of supercontinent, its breakup and divergence of continents. Our results show that cold downgoing flows aggregate continents into a supercontinent. After its formation, the convection pattern changes: the subduction zones at the edges of the supercontinent and typical relatively narrow mantle plumes in the subcontinental mantle arise. The lifetime of the supercontinent is about 550 Ma. Typical velocities for continents before collision are 3–10 cm/year, for supercontinent 0.5–1.5 cm/year and after the breakup 4–8 cm/year. Despite the small mobility of the supercontinent, there is no significant warming up of the subcontinental mantle. The temperature anomaly under supercontinent is less than + 50 K and the superplume does not arise. We obtain that the phase transitions at 410 km and 660 km and the eclogitization of the subducted oceanic crust affects the supercontinent cycle significantly. Our results demonstrate certain irregularity of supercontinent cycle. The typical shear stresses in the mantle are less than 30 MPa; in the subduction zones and on the continent borders they are 100–250 MPa. Before the breakup maximum shear stress generated in the supercontinent can reach 200 MPa. [ABSTRACT FROM AUTHOR]

Lytro cameras are equipped to capture 3D information in one exposure without the need for structured illumination, allowing greyscale depth maps of the captured image to be created using the Lytro desktop software. These consumer-grade light-field cameras (Lytro) provide a cost-effective method of measuring the depth of multiple objects which is suitable for many applications. But, the greyscale depth maps generated using the Lytro cameras are in relative depth scale and hence not suitable for engineering applications where absolute depth is essential. In this research, camera control variables, environmental sensitivity, depth distortion characteristics, and the effective working range of first- and second-generation Lytro cameras were evaluated. In addition, a depth measuring technique to deliver 3D output depth maps represented in SI units (metres) is discussed in detail exhibiting the suitability of consumer-grade Lytro cameras suitability in metrological applications without significant modifications. [ABSTRACT FROM AUTHOR]

This paper argues that recent topological expressions of surface in architecture have an intellectual lineage to late-modernism. Several key developments of that era challenged the limitations of a simplified Cartesian understanding of form. This paper commences with a discussion of Cartesian geometry in Modernism, relative to innovations in the building industry that promoted constancy, repetition and standardisation. Despite the same logic being transferred to digital working platforms where the architectural elements are normally designed as geometric prisms and their immediate derivatives, an interest in computation has enabled architecture to bypass orthogonal regularity. Concepts investigated during late-modernism—such as adaptability, disequilibrium, and smooth transitioning—are now central to performance and parametric-based design, examined through the interaction with data inputs, further pointing at critical updates of common software production tools. [ABSTRACT FROM AUTHOR]

We extend the notion of canonical measures to all (possibly non-compact) metric graphs. This will allow us to introduce a notion of "hyperbolic measures" on universal covers of metric graphs. Kazhdan's theorem for Riemann surfaces describes the limiting behavior of canonical (Arakelov) measures on finite covers in relation to the hyperbolic measure. We will prove a generalized version of this theorem for metric graphs, allowing any infinite Galois cover to replace the universal cover. We will show all such limiting measures satisfy a version of Gauss–Bonnet formula which, using the theory of von Neumann dimensions, can be interpreted as a "trace formula". In the special case where the infinite cover is the universal cover, we will provide explicit methods to compute the corresponding limiting (hyperbolic) measure. Our ideas are motivated by non-Archimedean analytic and tropical geometry. [ABSTRACT FROM AUTHOR]

The growing demand for prolonged fatigue life of automotive parts and components requires elaboration of their motion in Cartesian space having six degrees of freedom (DOF). Recently, the canonical Steward platform, consisting of six displacement sensors mounted on two parallel platforms, was introduced to comply with this request. In order to apply this pose sensor to automotive applications, the following two important matters are investigated in this study. First, update Jacobian is proposed as a faster and more stable numerical method to solve the forward kinematic problem without any iteration process. Second, the attachment position and initial configuration of the Stewart platform must be adjustable to avoid the interference with other components due to space constraints under the hood of automotive vehicle. In this case, however, the Jacobian matrix which converts six displacement components into a six DOF pose vector is prone to be ill-conditioned so that the converting accuracy becomes worse. The L1-norm of each row in the Jacobian matrix quantifies how much the error would be provoked according to the given kinematic geometry. Hence, it can be used here as a reliable error indicator. Furthermore, several numerical examples are discussed to demonstrate what to consider when designing a six DOF pose sensor for automotive applications. [ABSTRACT FROM AUTHOR]

For a sequence of continuous, monotone functions f1,…,fn:I→R (I is an interval) we define the mapping M:In→In as a Cartesian product of quasi-arithmetic means generated by fj-s. It is known that, for every initial vector, the iteration sequence of this mapping tends to the diagonal of In. We will prove that whenever all fj-s are C2 with nowhere vanishing first derivative, then this convergence is quadratic. Furthermore, the limit VarMk+1(v)(VarMk(v))2 will be calculated in a nondegenerated case. [ABSTRACT FROM AUTHOR]

In their classical work, Sammartino and Caflisch (Commun Math Phys 192(2):433-461, 1998a; Commun Math Phys 192(2):463-491, 1998b) proved the inviscid limit of the incompressible Navier-Stokes equations for well-prepared data with analytic regularity in the half-space. Their proof is based on the detailed construction of Prandtl’s boundary layer asymptotic expansions. In this paper, we give a direct proof of the inviscid limit for general analytic data without having to construct Prandtl’s boundary layer correctors. Our analysis makes use of the boundary vorticity formulation and the abstract Cauchy-Kovalevskaya theorem on analytic boundary layer function spaces that capture unbounded vorticity. [ABSTRACT FROM AUTHOR]

Thus HT ht is not constructible, nor is HT ht . Are you aware of the burgeoning movement since 2010 to replace the symbol HT ht with HT ht , because once around a circle is HT ht radians rather than the overweight expression HT ht ? Note that HT ht , HT ht , and HT ht are all congruent. [Extracted from the article]

Abstract: For finding global approximate solutions to an algebraic equation in n unknowns, the Hadamard open polygon for the case n = 1 and Hadamard polyhedron for the case n = 2 are used. The solutions thus found are transformed to the coordinate space by a translation (for n = 1) and by a change of coordinates that uses the curve uniformization (for n = 2). Next, algorithms for the local solution of the algebraic equation in the vicinity of its singular (critical) point for obtaining asymptotic expansions of one-dimensional and two-dimensional branches are presented for n = 2 and n = 3. Using the Newton polygon (for n = 2), the Newton polyhedron (for n = 3), and power transformations, this problem is reduced to situations similar to those occurring in the implicit function theorem. In particular, the local analysis of solutions to the equation in three unknowns leads to the uniformization problem of a plane curve and its transformation to the coordinate axis. Then, an asymptotic expansion of a part of the surface under examination can be obtained in the vicinity of this axis. Examples of such calculations are presented. [ABSTRACT FROM AUTHOR]