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Showing papers on "Hadamard transform published in 2021"



Journal ArticleDOI
TL;DR: In this article, the non-convex interval-valued functions for fuzzy-intervalvalued functions are introduced by means of fuzzy order relation, which is defined level-wise through Kulisch-Miranker order relation given on the interval space.
Abstract: In this paper, we introduce the non-convex interval-valued functions for fuzzy-interval-valued functions, which are called -convex fuzzy-interval-valued functions, by means of fuzzy order relation This fuzzy order relation is defined level-wise through Kulisch–Miranker order relation given on the interval space By using the -convexity concept, we present fuzzy-interval Hermite–Hadamard inequalities for fuzzy-interval-valued functions Several exceptional cases are debated, which can be viewed as useful applications Interesting examples that verify the applicability of the theory developed in this study are presented The results of this paper can be considered as extensions of previously established results

54 citations



Journal ArticleDOI
TL;DR: The main objective is to provide an efficient transmission and detection scheme with both spatial and temporal correlations in a massive MIMO connectivity scenario in which a large number of mobile devices are connected to a base station, while only a small portion are active at any given time.
Abstract: We address the joint device activity detection and channel estimation (JACE) problem in a massive MIMO connectivity scenario in which a large number of mobile devices are connected to a base station (BS), while only a small portion are active at any given time. The main objective is to provide an efficient transmission and detection scheme with both spatial and temporal correlations. We formulate JACE as a multiple measurement vector (MMV) problem with correlated entries in the vectors to be estimated. We propose an MMV form of the orthogonal approximate message passing algorithm (OAMP-MMV). We derive a group Gram-Schmidt orthogonalization (GGSO) procedure for the realization of OAMP-MMV. We outline a state evolution (SE) procedure for OAMP-MMV and examine its accuracy using numerical results. We also compare OAMP-MMV with existing alternatives, including AMP-MMV and GTurbo-MMV. We show that OAMP-MMV outperforms AMP-MMV when pilot sequences are generated using Hadamard pilot matrices. Such a pilot design is attractive due to the low-cost signal processing technique using the fast Hadamard transform (FHT). We also show that OAMP-MMV outperforms GTurbo-MMV in correlated channels.

51 citations


Book ChapterDOI
01 Jan 2021
TL;DR: This chapter is an introduction to shape and topology optimization, with a particular emphasis on the method of Hadamard for appraising the sensitivity of quantities of interest with respect to the domain, and on the level set method for the numerical representation of shapes and their evolutions.
Abstract: This chapter is an introduction to shape and topology optimization, with a particular emphasis on the method of Hadamard for appraising the sensitivity of quantities of interest with respect to the domain, and on the level set method for the numerical representation of shapes and their evolutions. At the theoretical level, the method of Hadamard considers variations of a shape as “small” deformations of its boundary; this results in a mathematically convenient and versatile notion of differentiation with respect to the domain, which has historically often been associated with “body-fitted” geometric optimization methods. At the numerical level, the level set method features an implicit description of the shape, which arises as the negative subdomain of an auxiliary “level set function”. This type of representation is well-known to be very efficient when it comes to describing dramatic evolutions of domains (including topological changes). The combination of these two ingredients is an ideal approach for optimizing both the geometry and the topology of shapes, and two related implementation frameworks are presented. The first and oldest one is a Eulerian shape capturing method, using a fixed mesh of a working domain in which the optimal shape is sought. The second and newest one is a Lagrangian shape tracking method, where the shape is exactly meshed at each iteration of the optimization process. In both cases, the level set algorithm is instrumental in updating the shapes, allowing for dramatic deformations between the iterations of the process, and even for topological changes. Most of our applicative examples stem from structural mechanics although some other physical contexts are briefly exemplified. Other topology optimization methods, like density-based algorithms or phase-field methods are also presented, at a lesser level of details, for comparison purposes.

47 citations


Journal ArticleDOI
TL;DR: The original secret color image can be successfully decrypted by the extraction of R, G, B components, inverse Arnold transformation, the correlated computation in SPI and inverse Hadamard transformation.

37 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed orthogonal time sequency multiplexing (OTSM), a single carrier modulation scheme that places information symbols in the delay-sequency domain.
Abstract: This paper proposes orthogonal time sequency multiplexing (OTSM), a novel single carrier modulation scheme that places information symbols in the delay-sequency domain followed by a cascade of time-division multiplexing (TDM) and Walsh-Hadamard sequence multiplexing. Thanks to the Walsh Hadamard transform (WHT), the modulation and demodulation do not require complex domain multiplications. For the proposed OTSM, we first derive the input-output relation in the delay-sequency domain and present a low complexity detection method taking advantage of zero-padding. We demonstrate via simulations that OTSM offers high performance gains over orthogonal frequency division multiplexing (OFDM) and similar performance to orthogonal time frequency space (OTFS), but at lower complexity owing to WHT. Then we propose a low complexity time-domain channel estimation method. Finally, we show how to include an outer error control code and a turbo decoder to improve error performance of the coded system.

31 citations


Journal ArticleDOI
TL;DR: In this paper, the stability and logarithmic decay of the solutions to fractional differential equations (FDEs) are studied and the asymptotic expansions of Mittag–Leffler function are discussed.
Abstract: In this paper, we study the stability and logarithmic decay of the solutions to fractional differential equations (FDEs). Both linear and nonlinear cases are included. And the fractional derivative is in the sense of Hadamard or Caputo–Hadamard with order $$\alpha \,(0<\alpha <1)$$ . The solutions can be expressed by Mittag–Leffler functions through applying the modified Laplace transform. In view of the asymptotic expansions of Mittag–Leffler function, we discuss the stability and logarithmic decay of the solution to FDEs in great detail.

28 citations


Journal ArticleDOI
01 Jan 2021
TL;DR: In this paper, the existence, uniqueness, and Hyers-Ulam stability of the coupled system of nonlinear fractional differential equations (FDEs) with multipoint and nonlocal integral boundary conditions are presented.
Abstract: This paper aims to present the existence, uniqueness, and Hyers-Ulam stability of the coupled system of nonlinear fractional differential equations (FDEs) with multipoint and nonlocal integral boundary conditions. The fractional derivative of the Caputo-Hadamard type is used to formulate the FDEs, and the fractional integrals described in the boundary conditions are due to Hadamard. The consequence of existence is obtained employing the alternative of Leray-Schauder, and Krasnoselskii's, whereas the uniqueness result, is based on the principle of Banach contraction mapping. We examine the stability of the solutions involved in the Hyers-Ulam type. A few examples are presented as an application to illustrate the main results. Finally, it addresses some variants of the problem.

27 citations



Journal ArticleDOI
TL;DR: In this paper, the authors discuss the solvability of Langevin equations with two Hadamard fractional derivatives and study the solutions of the equivalent Volterra integral integral.
Abstract: In this paper we discuss the solvability of Langevin equations with two Hadamard fractional derivatives. The method of this discussion is to study the solutions of the equivalent Volterra integral ...

Journal ArticleDOI
TL;DR: In this article, a conditional central limit theorem for data oblivious sketches is proved for Gaussian, Hadamard and Clarkson-Woodruff estimators, and the authors show that the best sketching algorithm in terms of mean square error is related to the signal to noise ratio in the source dataset.
Abstract: Sketching is a probabilistic data compression technique that has been largely developed in the computer science community. Numerical operations on big datasets can be intolerably slow; sketching algorithms address this issue by generating a smaller surrogate dataset. Typically, inference proceeds on the compressed dataset. Sketching algorithms generally use random projections to compress the original dataset and this stochastic generation process makes them amenable to statistical analysis. We argue that the sketched data can be modelled as a random sample, thus placing this family of data compression methods firmly within an inferential framework. In particular, we focus on the Gaussian, Hadamard and Clarkson-Woodruff sketches, and their use in single pass sketching algorithms for linear regression with huge $n$. We explore the statistical properties of sketched regression algorithms and derive new distributional results for a large class of sketched estimators. A key result is a conditional central limit theorem for data oblivious sketches. An important finding is that the best choice of sketching algorithm in terms of mean square error is related to the signal to noise ratio in the source dataset. Finally, we demonstrate the theory and the limits of its applicability on two real datasets.

Journal ArticleDOI
Sergey Bravyi1, Dmitri Maslov1
TL;DR: In this paper, the structural properties of the Clifford group were studied and a polynomial-time algorithm for computing the canonical form of Clifford operators was proposed, where the number of random bits consumed by the algorithm matches the information-theoretic lower bound.
Abstract: The Clifford group plays a central role in quantum randomized benchmarking, quantum tomography, and error correction protocols. Here we study the structural properties of this group. We show that any Clifford operator can be uniquely written in the canonical form $F_{1}HSF_{2}$ , where $H$ is a layer of Hadamard gates, $S$ is a permutation of qubits, and $F_{i}$ are parameterized Hadamard-free circuits chosen from suitable subgroups of the Clifford group. Our canonical form provides a one-to-one correspondence between Clifford operators and layered quantum circuits. We report a polynomial-time algorithm for computing the canonical form. We employ this canonical form to generate a random uniformly distributed $n$ -qubit Clifford operator in runtime $O(n^{2})$ . The number of random bits consumed by the algorithm matches the information-theoretic lower bound. A surprising connection is highlighted between random uniform Clifford operators and the Mallows distribution on the symmetric group. The variants of the canonical form, one with a short Hadamard-free part and one allowing a circuit depth $9n$ implementation of arbitrary Clifford unitaries in the Linear Nearest Neighbor architecture are also discussed. Finally, we study computational quantum advantage where a classical reversible linear circuit can be implemented more efficiently using Clifford gates, and show an explicit example where such an advantage takes place.

Journal ArticleDOI
TL;DR: In this article, the Atangana-Baleanu integral operator is used to obtain new integral inequalities of various Hadamard types with the help of this identity. But the main motivation in this paper is to prove a new and general integral identity and to obtain the new integral inequality.
Abstract: The main motivation in this article is to prove a new and general integral identity and to obtain new integral inequalities of various Hadamard types with the help of this identity. Some basic inequalities such as Holder, Young, power-mean and Jensen inequality have been used to obtain inequalities, and it has been determined that the main findings are generalizations and repetitions of many results that exist in the literature. Another impressive aspect of the study is that a new version of the Atangana–Baleanu integral operator is used, which is a very useful integral operator. We have given some simulations to demonsrate the consistency and harmony of this interesting operator for different values of the parameters.

Journal ArticleDOI
Jing Li1, Zong Meng1, Na Yin1, Zuozhou Pan1, Lixiao Cao1, Fengjie Fan1 
TL;DR: The experiment result shows that the composite fault diagnosis method of rolling bearing based on compressed sensing framework can improve the reconstruction precision and the separation stability of fault signal and can effectively extract fault characteristics and realize fault diagnosis.

Journal ArticleDOI
TL;DR: This work introduces the idea and concept of –polynomial –harmonic exponential type convex functions and elaborate the newly introduced idea by examples and some interesting algebraic properties, and establishes several new integral inequalities.
Abstract: In this work, we introduce the idea and concept of –polynomial –harmonic exponential type convex functions. In addition, we elaborate the newly introduced idea by examples and some interesting algebraic properties. As a result, several new integral inequalities are established. Finally, we investigate some applications for means. The amazing techniques and wonderful ideas of this work may excite and motivate for further activities and research in the different areas of science.

Journal ArticleDOI
TL;DR: This paper deals with the proximal point algorithm for finding a singularity of sum of a single-valuedvector field and a set-valued vector field in the setting of Hadamard manifolds.
Abstract: This paper deals with the proximal point algorithm for finding a singularity of sum of a single-valued vector field and a set-valued vector field in the setting of Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed. Applications to composite minimization problems and variational inequality problems are also presented.


Journal ArticleDOI
TL;DR: In this paper, the authors study the existence of solutions of equilibrium problems associated with pseudo-monotone bifunctions with suitable conditions on the bifunction in Hadamard spaces.
Abstract: As a continuation of previous work of the first author with Ranjbar [‘A variational inequality in complete CAT(0) spaces’, J. Fixed Point Theory Appl. 17 (2015), 557–574] on a special form of variational inequalities in Hadamard spaces, in this paper we study equilibrium problems in Hadamard spaces, which extend variational inequalities and many other problems in nonlinear analysis. In this paper, first we study the existence of solutions of equilibrium problems associated with pseudo-monotone bifunctions with suitable conditions on the bifunctions in Hadamard spaces. Then, to approximate an equilibrium point, we consider the proximal point algorithm for pseudo-monotone bifunctions. We prove existence of the sequence generated by the algorithm in several cases in Hadamard spaces. Next, we introduce the resolvent of a bifunction in Hadamard spaces. We prove convergence of the resolvent to an equilibrium point. We also prove -convergence of the sequence generated by the proximal point algorithm to an equilibrium point of the pseudo-monotone bifunction and also the strong convergence under additional assumptions on the bifunction. Finally, we study a regularization of Halpern type and prove the strong convergence of the generated sequence to an equilibrium point without any additional assumption on the pseudo-monotone bifunction. Some examples in fixed point theory and convex minimization are also presented.

Journal ArticleDOI
TL;DR: Ghulam Farid, Atiq Ur Rehman, Sidra Bibi, and Yu-Ming Chu as discussed by the authors have proposed a method to solve the problem of Mathematical Modeling and Analysis in Engineering.
Abstract: Ghulam Farid1,∗, Atiq Ur Rehman1, Sidra Bibi1 and Yu-Ming Chu2,3 1 Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan. 2 Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China. 3 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. China. * Correspondence: ghlmfarid@ciit-attock.edu.pk

Journal ArticleDOI
TL;DR: In this article, two efficient algorithms for solving variational inequality on Hadamard manifolds were proposed, inspired by Tseng's extragradient methods with new step sizes.
Abstract: This paper is devoted to two efficient algorithms for solving variational inequality on Hadamard manifolds. The algorithms are inspired by Tseng's extragradient methods with new step sizes, establi...

Journal ArticleDOI
TL;DR: In this article, the authors introduced new time scales for discrete convex functions and investigated the discrete fractional inequality of Hermite-Hadamard type for the left nabla and right delta fractional sums.
Abstract: We introduce new time scales on $\mathbb{Z}$ . Based on this, we investigate the discrete inequality of Hermite–Hadamard type for discrete convex functions. Finally, we improve our result to investigate the discrete fractional inequality of Hermite–Hadamard type for the discrete convex functions involving the left nabla and right delta fractional sums.


Journal ArticleDOI
TL;DR: This paper establishes formally a relationship between the Cauchy problem and an interface problem illustrated in a rectangular structure divided into two domains, and reformulates this inverse problem into a fixed point one, based on Steklov–Poincare operator.

Journal ArticleDOI
01 Jan 2021
TL;DR: In this article, the Hermite-Hadamard inequality for GC fractional integral operators has been established and a bound for the absolute difference between the two rightmost terms in the newly established Hermite Hadamard inequalities is obtained.
Abstract: This paper is concerned to establish an advanced form of the well-known Hermite-Hadamard (HH) inequality for recently-defined Generalized Conformable (GC) fractional operators. This form of the HH inequality combines various versions (new and old) of this inequality, containing operators of the types Katugampula, Hadamard, Riemann-Liouville, conformable and Riemann, into a single form. Moreover, a novel identity containing the new GC fractional integral operators is proved. By using this identity, a bound for the absolute of the difference between the two rightmost terms in the newly-established Hermite-Hadamard inequality is obtained. Also, some relations of our results with the already existing results are presented. Conclusion and future works are presented in the last section.

Journal ArticleDOI
TL;DR: In this article, a hybrid quantum-classical algorithm for simulating the dynamics of quantum systems is proposed, which takes the ansatz wave function as a linear combination of quantum states.
Abstract: Quantum simulation can help us study poorly understood topics such as high-temperature superconductivity and drug design. However, existing quantum simulation algorithms for current quantum computers often have drawbacks that impede their application. Here, we provide a hybrid quantum-classical algorithm for simulating the dynamics of quantum systems. Our approach takes the ansatz wave function as a linear combination of quantum states. The quantum states are fixed, and the combination parameters are variationally adjusted. Unlike existing variational quantum simulation algorithms, our algorithm does not require any classical-quantum feedback loop and by construction bypasses the barren plateau problem. Moreover, our algorithm does not require any complicated measurements such as the Hadamard test. The entire framework is compatible with existing experimental capabilities and thus can be implemented immediately.


Journal ArticleDOI
01 Jan 2021
TL;DR: In this paper, the Hermite-Hadamard-Mercer (HHM) type inequalities for convex functions were established by using generalized fractional integrals, such as Riemann-Liouville (RL) and conformable fractional integral types.
Abstract: In this work, we establish inequalities of Hermite-Hadamard-Mercer (HHM) type for convex functions by using generalized fractional integrals. The results of our paper are the extensions and refinements of Hermite-Hadamard (HH) and Hermite-Hadamard-Mercer (HHM) type inequalities. We discuss special cases of our main results and give new inequalities of HH and HHM type for different fractional integrals like, Riemann-Liouville (RL) fractional integrals, $ k $-Riemann-Liouville ($ k $-RL) fractional integrals, conformable fractional integrals and fractional integrals of exponential kernel.

Journal ArticleDOI
02 Sep 2021
TL;DR: In this paper, the existence, uniqueness and stability of solutions to a boundary value problem of nonlinear FDEs of variable order are established, and the Ulam-Hyers-Rassias stability of the given variable order Hadamard FBVP is examined.
Abstract: In this paper, the existence, uniqueness and stability of solutions to a boundary value problem of nonlinear FDEs of variable order are established. To do this, we first investigate some aspects of variable order operators of Hadamard type. Then, with the help of the generalized intervals and piecewise constant functions, we convert the variable order Hadamard FBVP to an equivalent standard Hadamard BVP of the fractional constant order. Further, two fixed point theorems due to Schauder and Banach are used and, finally, the Ulam–Hyers–Rassias stability of the given variable order Hadamard FBVP is examined. These results are supported with the aid of a comprehensive example.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the existence of solutions for Hadamard type two dimensional fractional functional integral equations on [ 1, b ] × [ 1, c ] and used the concept of measure of noncompactness and Darbo's fixed point theorem as the main tool to prove their results.
Abstract: In this article, we investigate the existence of solutions for Hadamard type two dimensional fractional functional integral equations on [ 1 , b ] × [ 1 , c ] . We use the concept of measure of non-compactness and Darbo’s fixed point theorem as the main tool to prove our results. Also, with the help of an example, we discuss the validity of our result.