Being a powerful strategy to preclude drag and achieve hydrodynamic invisibility, flow field manipulation is attracting widespread attention. In this investigation, we introduce a systematic set of arbitrary-space divide-and-conquer transformation st...
For the most popular method of scan formation in Optical Coherence Tomography (OCT) based on plane-parallel scanning of the illuminating beam, we present a compact but rigorous K-space description in which the spectral representation is used to descr...
The submodel of ideal gas motion being invariant with respect to the time translation and the space translation by one direct has 4 integrals in the case of vortex flows with the varying entropy. The system of nonlinear differential equations of the...
Cluster validity indices (CVIs) for evaluating the result of the optimal number of clusters are critical measures in clustering problems. Most CVIs are designed for typical data-type objects called certain data objects. Certain data objects only have...
The Hough transform is commonly used for detecting linear features within an image. A line is mapped to a peak within parameter space corresponding to the parameters of the line. By analysing the shape of the peak, or peak locus, within parameter spa...
In Electromagnetics, the field scattered by an ensemble of particles—of arbitrary size, shape, and material—can be obtained by solving the Lippmann–Schwinger equation. This singular vectorial integral equation is generally formulate...
In the following, isomorphism of an arbitrary finite group of symmetry, non-crystallographic symmetry (quaternion groups, Pauli matrices groups, and other abstract subgroups), in addition to the permutation group, are considered. Application of fini...
The tomography of a single quantum particle (i.e., a quantum wave packet) in an accelerated frame is studied. We write the Schrödinger equation in a moving reference frame in which acceleration is uniform in space and an arbitrary function of time. T...
The functional Schrödinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the formulation based on precanonical quantization. The previously established relationship bet...
In contemporary architectural design, a noticeable trend emerges in the meticulous planning of common areas, with an emphasis on fostering the free movements of users within these areas. It is important to consider the architectural elements that inf...
In this study, we investigate the upper- and lower-bound approximations of numerical eigenvalues derived by weak Galerkin spectral element methods on arbitrary convex quadrilateral meshes for the Laplace eigenvalue problem. Firstly, the Piola transfo...
The method proposed by Inomata and his collaborators allows us to transform a damped Caldirola–Kanai oscillator with a time-dependent frequency to one with a constant frequency and no friction by redefining the time variable, obtained by solving an E...
The main objective of the present paper is to provide a simple analytical solution for describing the expansion of a two-layer tube under plane-strain conditions for its subsequent use in the preliminary design of hydroforming processes. Each layer’s...
We review the canonical transformation in quantum physics known as the Bogoliubov transformation and present its application to the general theory of quantum field mixing and oscillations with an arbitrary number of mixed particles with either boson...
This paper extends the univariate Theory of Connections, introduced in (Mortari, 2017), to the multivariate case on rectangular domains with detailed attention to the bivariate case. In particular, it generalizes the bivariate Coons surface, introduc...
In this article, we propose a new path-conservative discontinuous Galerkin (DG) method to solve non-conservative hyperbolic partial differential equations (PDEs). In particular, the method here applies the one-stage ADER (Arbitrary DERivatives in spa...
We study an integral transform—here called the Master Integral Transform—in which the kernel is an arbitrary entire function of finite order. When the nonzero Taylor coefficients of the kernel have positive Beurling–Malliavin densit...
The empirical wavelet transform is an adaptive multi-resolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the detected partiti...
Reproducible crystallographic features between new phase and matrix are often observed during phase transformation, including orientation relationship, interfacial orientation, morphology, and so on. The geometrical matching in the interface is the k...
Positivity of a linear control system is interpreted as a symmetry with respect to transformations preserving the nonnegative cone of the state space. We study systems on arbitrary time scales and compare positivity criteria for different time scales...
This article deals with Lie algebra
The actual problem of structural monitoring and modeling of dynamic response from buried building is considered in the framework of arbitrary dynamic load. The results can be used for designing underground transport constructions, crossings, buried r...
In this work transformation electromagnetics/optics (TE/TO) were employed to realize a non-homogeneous, anisotropic material-embedded beam-steerer using both a single antenna element and an antenna array without phase control circuitry. Initially, th...
A disentanglement puzzle consists of mechanically interlinked pieces, and the puzzle is solved by disentangling one piece from another set of pieces. A string puzzle consists of strings entangled with one or more wooden pieces. We consider the genera...
Many urban applications require building polygons as input. However, manual extraction from point cloud data is time- and labor-intensive. Hough transform is a well-known procedure to extract line features. Unfortunately, current Hough-based approach...
The Synthetic Aperture Interferometric Radiometer Performance Simulator (SAIRPS) has been a three-year project sponsored by the European Space Agency (ESA) to develop a completely generic end-to-end performance simulator of arbitrary synthetic apertu...
The interpretation of three-dimensional (3-D) magnetotelluric (MT) data is usually based on the isotropic assumption of the subsurface structures, and this assumption could lead to erroneous interpretation in the area with considerable electrical ani...
In this work, we propose a hybrid control scheme to address the navigation problem for a team of disk-shaped robotic platforms operating within an obstacle-cluttered planar workspace. Given an initial and a desired configuration of the system, we dev...
This paper considers a 1D time-domain inverse scattering problem for the Helmholtz equation in which penetrable scatterers are to be determined from boundary measurements of the scattering data. It is formulated as a coefficient identification proble...
A special class of Physical Unclonable Functions (PUFs) referred to as strong PUFs can be used in novel hardware-based authentication protocols. Strong PUFs are required for authentication because the bit strings and helper data are transmitted openl...
The mechanical properties of anisotropic materials are generally characterized based on the orthotropy or transverse isotropy. However, the two-dimensional plane stress problems cannot comprehensively characterize the anisotropy of materials. In this...
An extended four-dimensional version of the traditional Petitot–Citti–Sarti model on contour completion in the visual cortex is examined. The neural configuration space is considered as the group of similarity transformations, denoted as...
This paper obtained a semianalytical solution for the P-wave scattering problem by an arbitrary-shaped canyon in a saturated half-space by using Biot’s theory, the wave function expansion method, and the moments method. Firstly, based on the Bi...
To enable the realization of ultra-low magnetic fields for scientific and technological research, magnetic shielding is required to create a space with low residual magnetic field and high shielding factors. The shielding factors of magnetic shields...
The goal of this paper is to investigate the following Abel’s integral equation of the second kind:
Spherical microphone arrays have been paid increasing attention for their ability to locate a sound source with arbitrary incident angle in three-dimensional space. Low-frequency sound sources are usually located by using spherical near-field acousti...
Uniform design is a powerful and robust experimental methodology that is particularly advantageous for multidimensional numerical integration and high-level experiments. As its applications expand across diverse disciplines, the theoretical foundatio...
Suppose
We employ another approach to quantize electromagnetic fields in the coordinate space, instead of the mode (or Fourier) space, such that local features of photons can be efficiently, physically, and more intuitively described. To do this, coordinate-...
Traditional operational calculus, while intuitive and effective in addressing problems in physical fractal spaces, often lacks the rigorous mathematical foundation needed for fractional operations, sometimes resulting in inconsistent outcomes. To add...
Sentiment Analysis is an essential research topic in the field of natural language processing (NLP) and has attracted the attention of many researchers in the last few years. Recently, deep neural network (DNN) models have been used for sentiment ana...
The construction of rational absolute nodal coordinate formulation (RANCF) elements is usually based on a linear transformation of non-uniform rational B-spline (NURBS) geometry. However, this linear transformation can lead to property transfer issue...
The expression of robot arm morphology is a critical foundation for achieving effective motion planning and collision avoidance in robotic systems. Traditional geometry-based approaches usually suffer from the contradiction between the high demand fo...
To better address the challenges of complex backgrounds, varying object sizes, and arbitrary orientations in remote sensing object detection tasks, this paper proposes a deformable split fusion method based on an improved RoI Transformer called RoI T...
The graph Hilbert transform (GHT) is a key tool in constructing analytic signals and extracting envelope and phase information in graph signal processing. However, its utility is limited by confinement to the graph Fourier domain, a fixed phase shift...
The creeping flow of a viscous fluid around a soft colloidal sphere rotating about a diameter normal to two planar walls at an arbitrary position between them is theoretically investigated in the steady limit of small Reynolds numbers. The fluid velo...
This paper is supposed to form a keystone towards a new and alternative approach to Fourier analysis over LCA (locally compact Abelian) groups G. In an earlier paper the author has already shown that one can introduce convolution and the Fourier&ndas...
Focused Ion Beam Scanning Electron Microscopy (FIB-SEM) tomography provides a stack of images that represent serial slices of the sample. These images are displaced relatively to each other, and an alignment procedure is required. Traditional methods...
Balancing efficiency and accuracy is often challenging in the numerical solution of three-dimensional (3D) point source acoustic wave equations for layered media. To overcome this, an efficient solution method in the spatial-wavenumber domain is prop...
This study presents the solution of the transient spatial problem of the impact of a moving source of heat flux induced by laser radiation on the surface of a half-space using the superposition principle and the method of transient functions. The sol...
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