Arbitrary Type Research Articles

Hilbert and Poincaré problems for semi-linear equations in rectifiable domains

The study of the boundary value problem with arbitrary measurable data originated in the dissertation of Luzin where he investigated the Dirichlet problem for harmonic functions in the unit disk. Recently, in \cite{R7}, we studied the Hilbert, Poincaré and Neumann boundary value problems with arbitrary measurable data for generalized analytic and generalized harmonic functions and provided applications to relevant problems in mathematical physics. The present paper is devoted to the study of the boundary value problem with arbitrary measurable boundary data in a domain with rectifiable boundary corresponding to semi-linear equation with suitable nonlinear source. We construct a completely continuous operator and generate nonclassical solutions to the Hilbert and Poincaré boundary value problems with arbitrary measurable data for Vekua type and Poisson equations, respectively. Based on that, we prove the existence of solutions of the Hilbert boundary value problem for the nonlinear Vekua type equation with arbitrary measurable data in a domain with rectifiable boundary. It is necessary to point out that our approach differs from the classical variational approach in PDE as it is based on the geometric interpretation of boundary values as angular (along non-tangential paths) limits. The latter makes it possible to also obtain a theorem on the boundary value problem for directional derivatives, and, in particular, of the Neumann problem with arbitrary measurable data for the Poisson equation with nonlinear sources in any Jordan domain with rectifiable boundary. As a result we arrive at applications to some problems of mathematical physics.

The application of upwind meshless approximation finite volume method to the convection dominated problems on the unstructured and deformed meshes

The primary objective of this research is to develop a finite volume method that can incorporate the most widely recognized upwind schemes using meshless techniques on an unstructured mesh. The recently developed Meshless Approximation Finite Volume Method (MAFVM) is expected to provide a solution to the convection–diffusion equation with an extremely high Pélect number, regardless of the type or quality of mesh, even when dealing with highly distorted meshes. By incorporating the local compactly supported radial basis functions differential quadrature method (LCRBFDQ), a meshless approximation technique, the field variables, flux, and gradient are directly approximated using information from neighboring scattered nodes. Building upon this concept, we propose two meshless approximation approaches for computing the flux and gradient within the framework of the finite volume method. Elliptic type problem on regular mesh is solved using the proposed MAFVM by different flux computation methods. Parameters for MAFVM that provide accurate and robust results are suggested. Next standard linear and second order upwind schemes as well as the well-known total variation diminishing (TVD) methods are integrated into the proposed MAFVM, using the developed flux calculation method to solve convection–diffusion problem with very high Pélect number on standard or highly deformed mesh. Accurate and robust results can be observed which show that the current MAFVM can provide an alternative and better way to deal with strong convection problem on meshes of arbitrary types by the proposed meshless flux computation methods.

Mixture Basis Function Approximation and Neural Network Embedding Control for Nonlinear Uncertain Systems with Disturbances

A neural network embedding learning control scheme is proposed in this paper, which addresses the performance optimization problem of a class of nonlinear system with unknown dynamics and disturbance by combining with a novel nonlinear function approximator and an improved disturbance observer (DOB). We investigated a mixture basic function (MBF) to approximate the unknown nonlinear dynamics of the system, which allows an approximation in a global scope, replacing the traditional radial basis function (RBF) neural networks technique that only works locally and could be invalid beyond some scope. The classical disturbance observer is improved, and some constraint conditions thus are no longer needed. A neural network embedding learning control scheme is exploited. An arbitrary type of neural network can be embedded into a base controller, and the new controller is capable of optimizing the control performance by tuning the parameters of neural network and satisfying the Lyapunov stability simultaneously. Simulation results verify the effectiveness and advantage of our proposed methods.

High SBS Threshold Fiber Laser With Spectral Management Using Binarized Multi-Tone Signal Modulation

In the high-power narrow-linewidth continuous fiber laser system based on the master oscillator power amplifier (MOPA) structure, the linewidth and spectral shape of the seed source are directly related to the SBS effect threshold which limits the maximum output power. It is currently under investigation which spectral shape has the highest laser power threshold. In this study, the spectral broadening and shape control of seed sources based on high-order phase modulation of binarized multi-tone signals is proposed. Combined with the heterodyne detected-based high-precision spectral measurement method, the measurement accuracy is improved from GHz to MHz level, which assists in optimizing the spectral shape. The broadened seed sources with rectangular, triangular, concave, and super-Gaussian spectra are experimentally demonstrated. And a maximum power of 2234 W is obtained with a rectangular spectrum with 10-GHz bandwidth. Theoretically, this scheme has multi-dimensional spectra tuning ability and can achieve arbitrary spectral types to explore the optimal seed source spectrum in diverse applications.

Інтервальна оцінка показників надійності за результатами випробувань компонентів складної системи

The goal of this work is to find the lower estimate of the no-failure probability (NFP) of a complex monotonic nonrecoverable system from the results of independent binomial tests of its components. Using the general-and-probabilistic method, the NFP is considered as a probability function polynomial, which is a linear homogeneous polynomial in each of the S variables where S is the number of system component types. Based on the method of confidence sets, the NFP lower estimate is found as the minimum of a function of an unknown multidimensional parameter at a probability of the aggregate test results (failure-free operation) of the system components equal to one minus the guaranteed confidence coefficient. The paper reports a system of equations, each of which for two component types relates the component reliability derivatives of the NFP (and one more equation relates the component reliability and the confidence coefficient). Conditions are found for the initial guess in a numerical solution of the above system of nonlinear equations (the number of the conditions is equal to the number of the component types minus one; each condition is a like sign for two functions each of which depends on the probability of the test results of a particular component type and the component reliability of this probability). In some specific cases, the program dimension can be reduced due to the simple structure of the probability function polynomial. The presented method gives a confidence reliability estimate with a guaranteed confidence coefficient for complex system that cannot be reduced to a serial-parallel or a parallel-serial structure and consist of components with an arbitrary type of failure time distribution. The method allows one to get an estimate at a small number of tests and a small number of failures or in their absence, which is of especial importance for high-reliability systems.

Overcoming Chip Shortages: Low-Cost Open-Source Parametric 3-D Printable Solderless SOIC to DIP Breakout Adapters

The COVID-19 pandemic exposed the vulnerability of global supply chains of many products. One area that requires improved supply chain resilience and that is of particular importance to electronic designers is the shortage of basic dual in-line package (DIP) electronic components commonly used for prototyping. This anecdotal observation was investigated as a case study of using additive manufacturing to enforce contact between premade, off-the-shelf conductors to allow for electrical continuity between two arbitrary points by examining data relating to the stock quantity of electronic components, extracted from Digi-Key Electronics. This study applies this concept using an open hardware approach for the design, testing, and use of a simple, parametric, 3-D printable invention that allows for small outline integrated circuit (SOIC) components to be used in DIP package circuits (i.e., breadboards, protoboards, etc.). The additive manufacture breakout board (AMBB) design was developed using two different open-source modelers, OpenSCAD and FreeCAD, to provide reliable and consistent electrical contact between the component and the rest of the circuit and was demonstrated with reusable 8-SOIC to DIP breakout adapters. The three-part design was optimized for manufacturing with RepRap-class fused filament 3-D printers, making the AMBB a prime candidate for use in distributed manufacturing models. The AMBB offers increased flexibility during circuit prototyping by allowing arbitrary connections between the component and prototyping interface as well as superior organization through the ability to color-code different component types. The cost of the AMBB is CAD $0.066/unit, which is a 94% saving compared to conventional PCB-based breakout boards. Use of the AMBB device can provide electronics designers with an increased selection of components for through-hole use by more than a factor of seven. Future development of AMBB devices to allow for low-cost conversion between arbitrary package types provides a path towards more accessible and inclusive electronics design as well as faster prototyping and technical innovation.

Object Detection Using Sim2Real Domain Randomization for Robotic Applications

Robots working in unstructured environments must be capable of sensing and interpreting their surroundings. One of the main obstacles of deep-learning-based models in the field of robotics is the lack of domain-specific labeled data for different industrial applications. In this article, we propose a sim2real transfer learning method based on domain randomization for object detection with which labeled synthetic datasets of arbitrary size and object types can be automatically generated. Subsequently, a state-of-the-art convolutional neural network, YOLOv4, is trained to detect the different types of industrial objects. With the proposed domain randomization method, we could shrink the reality gap to a satisfactory level, achieving 86.32% and 97.38% mAP50 scores, respectively, in the case of zero-shot and one-shot transfers, on our manually annotated dataset containing 190 real images. Our solution fits for industrial use as the data generation process takes less than 0.5 s per image and the training lasts only around 12 h, on a GeForce RTX 2080 Ti GPU. Furthermore, it can reliably differentiate similar classes of objects by having access to only one real image for training. To our best knowledge, this is the only work thus far satisfying these constraints.

Development of a general flow sweeping mixing model and application to a wire-wrapped assembly

Subchannel analysis is an essential tool for analyzing the thermal-hydraulic and safety characteristics during the design of nuclear reactor cores. In the present study, a general flow sweeping mixing model is proposed to describe the flow sweeping effect in subchannel analysis, and the model form can be applied to rod bundles with arbitrary types of spacers. As an example, the general flow sweeping mixing model is applied to a wire-wrapped assembly proposed by Shanghai Jiao Tong University. In this example, the model factors are derived from numerical results, and the model coefficient is determined by experimental data. The model is evaluated by comparing it with existing models and experiment data, and the comparison results show the superiority of the new model. The crossflow rate of subchannel gaps caused by wire along the axial direction can be estimated by new model. The present study provides a new idea for the development of the flow sweeping mixing model used in subchannel analysis.

Privacy-preserving Federated Learning and its application to natural language processing

State-of-the-art edge devices are capable of not only inferring machine learning (ML) models but also training them on the device with local data. When this local data is sensitive, privacy becomes a crucial property that must be addressed. This implies that sharing data with a server for training a model is undesirable and should be avoided. The Federated Learning (FL) approach can help in these situations, however, FL alone is still not the ultimate tool to solve all challenges, especially when privacy is a major concern. We propose a privacy-preserving FL framework, which leverages the concepts of bitwise quantization, local differential privacy (LDP), and feature hashing for input representation in the collaborative training of ML models. In our approach, the local model updates are first quantized, then a randomized-response technique is applied on the resulting update vector.Although our proposed framework functions with arbitrary types of input features, we emphasize its usability with natural language data. The text input on the client-side is encoded using a rolling-hash-based representation, which provides a combined solution for the high resource demands of embedding algorithms and the privacy concerns of sharing sensitive data. We evaluate our method in a sentiment analysis task using the IMDB Movie Reviews dataset as well as a rating prediction task with the MovieLens dataset augmented with additional movie keywords. We demonstrate that our approach is a feasible solution for private language processing tasks on edge devices without the use of resource-hungry language models or privacy-violating collection of client data.

PBW theory for quantum affine algebras

Let U_q'(\mathfrak{g}) be a quantum affine algebra of arbitrary type and let \mathscr{C}_\mathfrak{g}^0 be Hernandez-Leclerc’s category. We can associate the quantum affine Schur–Weyl duality functor \mathcal{F}_\mathcal{D} to a duality datum \mathcal{D} in \mathscr{C}_\mathfrak{g}^0 . In this paper, we introduce the notion of a strong (complete) duality datum \mathcal{D} and prove that, when \mathcal{D} is strong, the induced duality functor \mathcal{F}_\mathcal{D} sends simple modules to simple modules and preserves the invariants \Lambda , \tilde\Lambda and \Lambda^\infty introduced by the authors. We next define the reflections \mathscr{S}_k and \mathscr{S}^{-1}_k acting on strong duality data \mathcal{D} . We prove that if \mathcal{D} is a strong (resp.\ complete) duality datum, then \mathscr{S}_k(\mathcal{D}) and \mathscr{S}_k^{-1}(\mathcal{D}) are also strong (resp. complete) duality data. This allows us to make new strong (resp. complete) duality data by applying the reflections \mathscr{S}_k and \mathscr{S}^{-1}_k from known strong (resp. complete) duality data. We finally introduce the notion of affine cuspidal modules in \mathscr{C}_\mathfrak{g}^0 by using the duality functor \mathcal{F}_\mathcal{D} , and develop the cuspidal module theory for quantum affine algebras similar to the quiver Hecke algebra case. When \mathcal{D} is complete, we show that all simple modules in \mathscr{C}_\mathfrak{g}^0 can be constructed as the heads of ordered tensor products of affine cuspidal modules. We further prove that the ordered tensor products of affine cuspidal modules have the unitriangularity property. This generalizes the classical simple module construction using ordered tensor products of fundamental modules.

Mixed Eulerian Numbers and Peterson Schubert Calculus

Abstract Let $\Phi $ be a root system. Postnikov introduced and studied the mixed $\Phi $-Eulerian numbers. These numbers indicate the mixed volumes of $\Phi $-hypersimplices. As specializations of these numbers, one can obtain the usual Eulerian numbers, the Catalan numbers, and the binomial coefficients. Recent work of Berget–Spink–Tseng gave a simple computation for the mixed $\Phi $-Eulerian numbers when $\Phi $ is of type $A$. In this paper, we connect a relation between mixed $\Phi $-Eulerian numbers and Peterson Schubert calculus. By using the connection, we provide a combinatorial model for the computation of Berget–Spink–Tseng in terms of left–right diagrams that were introduced by Abe–Horiguchi–Kuwata–Zeng for the purpose of Peterson Schubert calculus. We also derive a simple computation for the mixed $\Phi $-Eulerian numbers in arbitrary Lie types from Peterson Schubert calculus.

Automated design of freeform imaging systems for automotive heads-up display applications.

The freeform imaging system is playing a significant role in developing an optical system for the automotive heads-up display (HUD), which is a typical application of augmented reality (AR) technology. There exists a strong necessity to develop automated design algorithms for automotive HUDs due to its high complexity of multi-configuration caused by movable eyeballs as well as various drivers' heights, correcting additional aberrations introduced by the windshield, variable structure constraints originated from automobile types, which, however, is lacking in current research community. In this paper, we propose an automated design method for the automotive AR-HUD optical systems with two freeform surfaces as well as an arbitrary type of windshield. With optical specifications of sagittal and tangential focal lengths, and required structure constraints, our given design method can generate initial structures with different optical structures with high image quality automatically for adjusting the mechanical constructions of different types of cars. And then the final system can be realized by our proposed iterative optimization algorithms with superior performances due to the extraordinary starting point. We first present the design of a common two-mirror HUD system with longitudinal and lateral structures with high optical performances. Moreover, several typical double mirror off-axis layouts for HUDs were analyzed from the aspects of imaging performances and volumes. The most suitable layout scheme for a future two-mirror HUD is selected. The optical performance of all the proposed AR-HUD designs for an eye-box of 130 mm × 50 mm and a field of view of 13° × 5° is superior, demonstrating the feasibility and superiority of the proposed design framework. The flexibility of the proposed work for generating different optical configurations can largely reduce the efforts for the HUD design of different automotive types.

On congruences and linear relations for Drinfeld modular forms of level $\Gamma_{0}(T)$, arbitrary type

In [Cho09], Choi studied congruences of coefficients (modulo $T^{q}-T$) for Drinfeld modular forms of level $\Gamma_{0}(T)$, trivial type and the linear relations between the initial coefficients of those. In this article, we generalize these results for level $\Gamma_{0}(T)$, arbitrary type.

Making a Type Difference: Subtraction on Intersection Types as Generalized Record Operations

In programming languages with records, objects, or traits, it is common to have operators that allow dropping, updating or renaming some components. These operators are useful for programmers to explicitly deal with conflicts and override or update some components. While such operators have been studied for record types, little work has been done to generalize and study their theory for other types. This paper shows that, given subtyping and disjointness relations, we can specify and derive algorithmic implementations for a general type difference operator that works for other types, including function types, record types and intersection types. When defined in this way, the type difference algebra has many desired properties that are expected from a subtraction operator. Together with a generic merge operator, using type difference we can generalize many operations on records formalized in the literature. To illustrate the usefulness of type difference we create an intermediate calculus with a rich set of operators on expressions of arbitrary type, and demonstrate applications of these operators in CP , a prototype language for Compositional Programming . The semantics of the calculus is given by elaborating into a calculus with disjoint intersection types and a merge operator. We have implemented type difference and all the operators in the CP language. Moreover, all the calculi and related proofs are mechanically formalized in the Coq theorem prover.

Vibration of orthotropic doubly curved panel with a set of inclusions of arbitrary configuration taking into account distributed load on the surface of the panel

In the framework of the refined theory, which takes into account transverse shear deformation, the solution of the problem on the steady state vibrations of the orthotropic doubly curved panel with the arbitrary number of massive absolutely rigid inclusions of the arbitrary configuration that penetrate the panel through all its thickness taking into account harmonic in time arbitrary distributed external load on the surface of the panel is constructed. Inclusions have different types of connections with the panel and are subjected to the action of different systems of harmonic in time external forces with the principal vectors normal to the middle surface of the panel and principal moments about the centers of masses of the inclusions equal to zero. Inclussions are assumed to perform predominantly translational motion along the normal direction to the middle surface of the panel. External boundary of the panel is of arbitrary shape and different types of harmonic in time boundary conditions are considered on its contours. The solution is built on the basis of the indirect boundary elements method. The sequential approach to the representation of the Green’s functions is used. Integral equations are solved by thecollocation method.

Comparison of profile-likelihood-based confidence intervals with other rank-based methods for the two-sample problem in ordered categorical data

ABSTRACT For ordered categorical data from randomized clinical trials, the relative effect, the probability that observations in one group tend to be larger, has been considered appropriate for a measure of an effect size. Although the Wilcoxon–Mann–Whitney test is widely used to compare two groups, the null hypothesis is not just the relative effect of 50%, but the identical distribution between groups. The null hypothesis of the Brunner–Munzel test, another rank-based method used for arbitrary types of data, is just the relative effect of 50%. In this study, we compared actual type I error rates (or 1 – coverage probability) of the profile-likelihood-based confidence intervals for the relative effect and other rank-based methods in simulation studies at the relative effect of 50%. The profile-likelihood method, as with the Brunner– Munzel test, does not require any assumptions on distributions. Actual type I error rates of the profile-likelihood method and the Brunner–Munzel test were close to the nominal level in large or medium samples, even under unequal distributions. Those of the Wilcoxon–Mann–Whitney test largely differed from the nominal level under unequal distributions, especially under unequal sample sizes. In small samples, the actual type I error rates of Brunner–Munzel test were slightly larger than the nominal level and those of the profile-likelihood method were even larger. We provide a paradoxical numerical example: only the Wilcoxon–Mann–Whitney test was significant under equal sample sizes, but by changing only the allocation ratio, it was not significant but the profile-likelihood method and the Brunner–Munzel test were significant. This phenomenon might reflect the nature of the Wilcoxon–Mann–Whitney test in the simulation study, that is, the actual type I error rates become over and under the nominal level depending on the allocation ratio.

Two-port parameters of autotransformer discrete alternating voltage regulators

The present paper is dedicated to an unusual analysis of an autotransformer discrete alternating voltage regulator presented as a two-port with a load. The main purpose of the study is to determine the different sets of parameters (matrices) of this two-port – ABCD, B–, H-, G-, Z-, Y-parameters and the characteristic parameters. A Matlab simulation model of the autotransformer discrete alternating voltage regulator with four commutators, realized by thyristor switches, corresponding to different supply voltages, is used for the analysis. The non-linearities of the regulator’s circuit have been considered in the model. The received results were experimentally verified in the case of an active load and a good coincidence less than 1% was achieved. These parameters can be used for quick and accurate analysis of such a device in case of arbitrary type of the load – active, inductive or capacitive. The obtained results could be used to improve the methodologies for designing such regulators.

Extremely asymmetric sawtooth potential in the ratchet theory

AbstractWe present a review of analytical approaches involved in developing the ratchet theory, which are based on the model of extremely asymmetric sawtooth potential. Analytical expressions are given for the average velocity of ratchets which operate in various motion modes, namely, motion induced by dichotomous half‐period shifts of potential profiles, adiabatic and high‐temperature modes, and motion induced by small fluctuations of an arbitrary type. The presence of jumps in the periodic extremely asymmetric sawtooth potential profile leads to a number of features of the obtained solutions which follow from the competition of the reverse sliding time tending to infinity with high fluctuation frequencies. The resulting dependences of the average velocity on the ratchet parameters clearly demonstrate that the motion direction can be controlled by tuning the frequency and temperature. The heuristic value of the presented models for controlling nanoparticle transport is discussed.

Intrinsic anomalous spin Hall effect

Charge-spin interconversion in magnetic materials is investigated by using the first-principles calculations. In addition to the conventional spin Hall effect (SHE) that requires mutual orthogonality of the charge current, spin-flow direction, and spin polarization, the recently proposed anomalous SHE (ASHE) is confirmed in Mn2Au and WTe2. The interaction of the order parameter with conduction electrons leads to sizeable non-zero spin Berry curvatures that give rise to anomalous spin Hall conductivity (ASHC). Our calculations show that the ASHE is intrinsic and originates from the order-parameter-controlled spin-orbit interaction, which generates an extra anomalous effective field. A useful relationship among the order parameter, the spin Berry curvature, and the ASHC is revealed. Our findings provide a new avenue for generating and detecting arbitrary types of spin currents.

Emission of gravitational waves by superconducting cosmic strings

We study the gravitational radiation emission efficiency Γ of superconducting cosmic strings. We demonstrate, by using a solvable model of transonic strings, that the presence of a current leads to a suppression of the gravitational emission of cusps, kinks and different types of loops. We also show that, when a current is present, the spectrum of emission of loops with cusps is exponentially suppressed as the harmonic mode increases, thus being significantly different from the power law spectrum of currentless loops. Furthermore, we establish a phenomenological relationship between Γ and the value of the current on cosmic strings. We conjecture that this relation should be valid for an arbitrary type of current-carrying string. We use this result to study the potential impact of current on the stochastic gravitational wave background generated by cosmic strings with additional degrees of freedom and show that both the amplitude and shape of the spectrum may be significantly affected.