Bonnesen-style symmetric mixed inequalities by Pengfu Wang, Miao Luo, Jiazu Zhou

“…Via the known kinematic formulae of Poincaré and Blaschke in integral geometry, we obtain some Bonnesen-style symmetric mixed inequalities. …”
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Kinematic space and the orbit method by Robert F. Penna, Claire Zukowski

“…The orbit method extends the kinematic space dictionary, which was originally motivated through connections to integral geometry, by directly translating geometrical properties of holographic auxiliary spaces into statements about the representation theory of the conformal group.…”
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Analytical model for effects of capsule shape on the healing efficiency in self-healing materials. by Zhong Lv, Songpeng Li, Huisu Chen

“…The focus of this contribution is the description of the effects of capsule shape on the efficiency of healing agent released in capsule-based self-healing material within the framework of the theory of geometrical probability and integral geometry. Analytical models are developed to characterize the amount of healing agent released per crack area from capsules for an arbitrary crack intersecting with capsules of various shapes in a virtual capsule-based self-healing material. …”
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THE DEVELOPMENT OF STUDENTS APPLIED MATHEMATICAL THINKING IN TEACHING INVERSE AND ILL-POSED PROBLEMS by V S Kornilov

“…Among them, spectral analysis, the method of Volterra operator equations, Sobolev method, method of scales of Banach spaces of analytic functions, the method of integral geometry, the method of tensor analysis, methods of computational mathematics and other mathematical methods.…”
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A Dual of the Chow Transformation by Méo Michel

“…In such a way we complete the general scheme of integral geometry for the Chow transformation. On another hand we prove the existence of a well defined closed positive conormal current associated to every closed positive current on the projective space. …”
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An Effective SEM-Based Image Analysis System for Quantitative Mineralogy by R.P. King, C.L. Schneider

“…Existing systems make no provision for effective stereological analysis of image data nor for the interpretation of microstructure using models based on stochastic and integral geometry. This paper describes the development of an image analysis system based on an SEM equipped with secondary electron and back-scattered electron detectors, an image memory for the storage of digital images captured at slow scan speeds and a SUN workstation for image processing and image analysis. …”
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Global optimization using random embeddings by Cartis, C, Massart, E, Otemissov, A

“…We propose a random-subspace algorithmic framework for global optimization of Lipschitz-continuous objectives, and analyse its convergence using novel tools from conic integral geometry. X-REGO randomly projects, in a sequential or simultaneous manner, the high-dimensional original problem into low-dimensional subproblems that can then be solved with any global, or even local, optimization solver. …”

Quantitative solution on dosage of repair agent for healing of cracks in materials: short capsule model vs. two-dimensional crack pattern by Lv Zhong, Chen Huisu, Yuan Haifeng

“…Then, from the viewpoint of geometrical probability, the theoretical solutions on the exact dosage of capsules required are developed for different types of crack models via the knowledge of integral geometry and the concepts of probability distribution. …”
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The role of Minkowski functionals in the thermodynamics of two-phase systems by Gerhard Eder

“…Within this work quite old concepts from integral geometry are applied to classical equilibrium thermodynamics of two-phase systems. …”
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Neural network-based top tagger with two-point energy correlations and geometry of soft emissions by Amit Chakraborty, Sung Hak Lim, Mihoko M. Nojiri, Michihisa Takeuchi

“…The new set of IRC unsafe variables can be described by Minkowski functionals from integral geometry. To integrate these features into a single framework, we reintroduce two-point energy correlations in terms of a graph neural network and provide the other features to the network afterward. …”
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Conformal Field Theories in Six-Dimensional Twistor Space by Mason, L, Reid-Edwards, R, Taghavi-Chabert, A

“…We also develop the theory of Sparling's `\Xi-transform', the analogous totally real split signature story based now on real integral geometry where cohomology no longer plays a role. …”

TO THE QUESTION OF UNIQUENESS OF DEGENERATE SINGULAR INTEGRAL EQUATIONS SOLUTIONS by I. V. Boykov, N. Yu. Kudryashova, A. A. Shaldaeva

“…The proposed results can be directly used in solving many problems of physics and technology, in particular, in the problems of integral geometry, aerodynamics, and hydrodynamics. It is of interest to extend these results to degenerate polysingular integral equations.…”

AN APPROXIMATE METHODS FOR SOLVING POLYSINGULAR INTEGRAL EQUATIONS IN DEGENERATE CASES by I. V. Boykov, N. Yu. Kudryashova, A. A. Shaldaeva

“…The proposed results can be directly used in solving many problems of physics and technology, in particular, in problems of integral geometry, aerodynamics, hydrodynamics. It is of interest to extend these results to degenerate multidimensional singular integral equations.…”

The jump and stagnation of mass with speed by Jun Dong, Na Dong

“…Abstract In the general theory of relativity, the four‐dimensional space‐time of describing a mass body accelerated motion or in a gravitational field, although it is a curved Riemannian geometric space from the perspective of “integral geometry”, but for any instantaneous position of the moving mass body, there is a local Flat Space of Riemannian geometric space. …”
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Closed-Form UAV LoS Blockage Probability in Mixed Ground- and Rooftop-Mounted Urban mmWave NR Deployments by Vyacheslav Begishev, Dmitri Moltchanov, Anna Gaidamaka, Konstantin Samouylov

“…In our study, we use the tools of integral geometry to characterize connectivity properties of UAVs in terrestrial urban deployments of mmWave NR systems using UAV line-of-sight (LoS) blockage probability as the main metric of interest. …”
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Dimensionality reduction techniques for global optimization by Otemissov, A

“…For Lipschitz continuous objectives, we develop a novel analysis that estimates the probability of success of the feasible randomly reduced subproblems based on connections to the field of conic integral geometry. To evaluate the quality of our bound, we compare it to the success of uniform sampling, in the asymptotic regime. …”

Effect of pressure on structure and properties of lost foam casting of al-11si cast alloy by Niakan, Aliasghar, Idris, Mohd. Hanafi, Karimian, Majid, Ourdjini, Ali

“…The study investigated the effect of pressure on casting integrity-geometry, eutectic silicon spacing, particle roundness and hardness. …”

Induced geometry from disformal transformation by Fang-Fang Yuan, Peng Huang

“…The new geometry obtained here can be considered as a generalization of Weyl integrable geometry. Based on these results, we further propose a geometry which is naturally a generalization of Weyl geometry.…”
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Geometry and complexity of path integrals in inhomogeneous CFTs by Paweł Caputa, Ian MacCormack

“…After setting up and solving the general optimization problem, we study specific examples, including the Möbius, SSD and Rainbow deformed CFTs, and analyze path integral geometries and complexity for universal classes of states in these models. …”
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Correlating 3D Experiments with Dynamic Figures Analysis by Liliana Saidon

“…Integrating geometry, algebra and calculus in computer-mediated activities by means of a free software such as GeoGebra is a challenge for all participants involved, and requires a reciprocal conceptual exploratory alternative for the teaching and learning of mathematics at pre-universitary level. …”
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