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Journal articles on the topic 'Hadamard'

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Published: 4 June 2021

Last updated: 1 June 2024

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1

Almutairi, Ohud, and Adem Kılıçman. "New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals." Symmetry 12, no. 4 (April 5, 2020): 568. http://dx.doi.org/10.3390/sym12040568.

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In this paper, a new identity for the generalized fractional integral is defined. Using this identity we studied a new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. This fractional integral generalizes Riemann-Liouville and Hadamard’s integral, which possess a symmetric property. We derive trapezoid and mid-point type inequalities connected to this generalized Hermite-Hadamard inequality.

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2

Sudsutad, Weerawat, Sotiris K. Ntouyas, and Jessada Tariboon. "Fractional Integral Inequalities via Hadamard’s Fractional Integral." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/563096.

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We establish new fractional integral inequalities, via Hadamard’s fractional integral. Several new integral inequalities are obtained, including a Grüss type Hadamard fractional integral inequality, by using Young and weighted AM-GM inequalities. Many special cases are also discussed.

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3

Pachpatte, B. G. "A note on Hadamard type integral inequalities involving several log-convex functions." Tamkang Journal of Mathematics 36, no. 1 (March 31, 2005): 43–47. http://dx.doi.org/10.5556/j.tkjm.36.2005.134.

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In this note, two new inegral inequalities of Hadamard type involving several differentiable log-convex functions are given. Two refinements of Hadamard's integral inequality for log-convex functions recently established by Dragomir are shown to be recaptured as special instances.

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4

Muddassar, Muhammad, Muhammad Iqbal, Tahira Jabeen, and Ghulam haider. "A Stimulus Generalization of Double Integral Inequalities by the way of Fractional Integrals." International Journal of Emerging Multidisciplinaries: Mathematics 1, no. 1 (January 14, 2022): 66–74. http://dx.doi.org/10.54938/ijemdm.2022.01.1.19.

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This study presents some of the latest results annexed to Hermite Hadamard inequality by utilizing double integrals by the way of Riemann-Liouville fractional integrals. Another aim of this article is to generalize some of the recent developments on Hermite Hadamard's type inequalities.

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5

Kuperberg, Vivian. "Hadamard Matrices Modulopand Small Modular Hadamard Matrices." Journal of Combinatorial Designs 24, no. 9 (May 6, 2016): 393–405. http://dx.doi.org/10.1002/jcd.21522.

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6

Arma, Sovia, Yanita Yanita, and Nova Noliza Bakar. "SIFAT-SIFAT OPERASI HADAMARD PADA MATRIKS." Jurnal Matematika UNAND 7, no. 4 (February 19, 2019): 61. http://dx.doi.org/10.25077/jmu.7.4.61-68.2018.

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Tulisan ini membahas tentang sifat-sifat operasi Hadamard pada matriks, dimana operasi Hadamard merupakan operasi perkalian elemen-elemen yang bersesuaian dari dua matriks A dan B yang berukuran sama. Sifat-sifat operasi Hadamard yang dibahas pada tulisan ini adalah sifat-sifat dasar operasi Hadamard dan sifat-sifat operasi Hadamard terhadap definit positif dan definit taknegatif.Kata Kunci: Matriks, Operasi Hadamard, Sifat-Sifat Dasar, Definit Positif, Definit Taknegatif

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7

Kharaghani, Hadi, Thomas Pender, Caleb Van't Land, and Vlad Zaitsev. "Bush-type Butson Hadamard matrices." Glasnik Matematicki 58, no. 2 (December 27, 2023): 247–57. http://dx.doi.org/10.3336/gm.58.2.07.

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Bush-type Butson Hadamard matrices are introduced. It is shown that a nonextendable set of mutually unbiased Butson Hadamard matrices is obtained by adding a specific Butson Hadamard matrix to a set of mutually unbiased Bush-type Butson Hadamard matrices. A class of symmetric Bush-type Butson Hadamard matrices over the group \(G\) of \(n\)-th roots of unity is introduced that is also valid over any subgroup of \(G\). The case of Bush-type Butson Hadamard matrices of even order will be discussed.

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8

İşcan, İmdat. "Hermite-Hadamard and Simpson Type Inequalities for Differentiable P-GA-Functions." International Journal of Analysis 2014 (May 22, 2014): 1–6. http://dx.doi.org/10.1155/2014/125439.

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The author introduces the concept of the P-GA-functions, gives Hermite-Hadamard's inequalities for P-GA-functions, and defines a new identity. By using this identity, the author obtains new estimates on generalization of Hadamard and Simpson type inequalities for P-GA-functions. Some applications to special means of real numbers are also given.

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9

Kahane, Jean-Pierre. "Jacques Hadamard." Mathematical Intelligencer 13, no. 1 (December 1991): 23–29. http://dx.doi.org/10.1007/bf03024068.

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10

Blanchet, Luc, and Guillaume Faye. "Hadamard regularization." Journal of Mathematical Physics 41, no. 11 (November 2000): 7675–714. http://dx.doi.org/10.1063/1.1308506.

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11

Ivanov, D. N. "Hadamard algebras." Mathematical Notes 96, no. 1-2 (July 2014): 199–203. http://dx.doi.org/10.1134/s0001434614070207.

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12

Flannery, D. L. "Cocyclic Hadamard Matrices and Hadamard Groups Are Equivalent." Journal of Algebra 192, no. 2 (June 1997): 749–79. http://dx.doi.org/10.1006/jabr.1996.6949.

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13

Dehghanian, Mehdi, Yamin Sayyari, and Choonkil Park. "Hadamard homomorphisms and Hadamard derivations on Banach algebras." Miskolc Mathematical Notes 24, no. 1 (2023): 129. http://dx.doi.org/10.18514/mmn.2023.3928.

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14

Chen, Yuming. "Order-six complex hadamard matrices constructed by Schmidt rank and partial transpose in operator algebra." Theoretical and Natural Science 34, no. 1 (May 10, 2024): 249–61. http://dx.doi.org/10.54254/2753-8818/34/20241113.

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Hadamard matrices play a key role in the study of algebra and quantum information theory, and it is an open problem to characterize 6 6 Hadamard matrices. In this paper, we investigate the problem in terms of the Schmidt rank. The primary achievement of this paper lies in establishing a systematic approach to generate 6 6 Hadamard matrices and H-2 reducible matrices through partial transpose. First, if the Schmidt rank of a Hadamard matrix is at most three, then the partial transpose of the Hadamard matrix is also a Hadamard matrix. Conversely, if the Schmidt rank is four, then the partial transpose is no longer a Hadamard matrix. Second, we discuss the relationship between Schmidt rank and H-2 reducible matrices. We prove Hadamard matrices with Schmidt-rank-one are all H-2 reducible, and prove that some Schmidt-rank-two matrices are H-2 reducible. Finally, we confirm that the partial transpose of an H-2 reducible Schmidt-rank-one or two Hadamard matrix remains H-2 reducible.

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15

Álvarez, Víctor, José Andrés Armario, María Dolores Frau, Félix Gudiel, María Belén Güemes, and Amparo Osuna. "Hadamard Matrices with Cocyclic Core." Mathematics 9, no. 8 (April 14, 2021): 857. http://dx.doi.org/10.3390/math9080857.

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Since Horadam and de Launey introduced the cocyclic framework on combinatorial designs in the 1990s, it has revealed itself as a powerful technique for looking for (cocyclic) Hadamard matrices. Ten years later, the series of papers by Kotsireas, Koukouvinos and Seberry about Hadamard matrices with one or two circulant cores introduced a different structured approach to the Hadamard conjecture. This paper is built on both strengths, so that Hadamard matrices with cocyclic cores are introduced and studied. They are proved to strictly include usual Hadamard matrices with one and two circulant cores, and therefore provide a wiser uniform approach to a structured Hadamard conjecture.

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16

Jung, Chahnyong, Ghulam Farid, Muhammad Yussouf, and Kamsing Nonlaopon. "Hadamard-Type Inequalities for Generalized Integral Operators Containing Special Functions." Symmetry 14, no. 3 (February 28, 2022): 492. http://dx.doi.org/10.3390/sym14030492.

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Convex functions are studied very frequently by means of the Hadamard inequality. A symmetric function leads to the generalization of the Hadamard inequality; the Fejér–Hadamard inequality is one of the generalizations of the Hadamard inequality that holds for convex functions defined on a finite interval along with functions which have symmetry about the midpoint of that finite interval. Lately, integral inequalities for convex functions have been extensively generalized by fractional integral operators. In this paper, inequalities of Hadamard type are generalized by using exponentially (α, h-m)-p-convex functions and an operator containing an extended generalized Mittag-Leffler function. The obtained results are also connected with several well-known Hadamard-type inequalities.

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17

Harms, B. K., J. B. Park, and S. A. Dyer. "On the Use of Fast Hadamard Transforms for Spectrum Recovery in Hadamard Transform Spectroscopy." Applied Spectroscopy 46, no. 9 (September 1992): 1358–61. http://dx.doi.org/10.1366/0003702924123700.

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The spectrum-recovery step in Hadamard transform spectroscopy is commonly implemented with a fast Hadamard transform (FHT). When the Hadamard or simplex matrix corresponding to the mask does not have the same ordering as the Hadamard matrix corresponding to the FHT, a modification is required. When the two Hadamard matrices are in the same equivalence class, this modification can be implemented as a permutation scheme. This paper investigates permutation schemes for this application. The investigation clarifies inaccurate claims about the applicability of existing methods; reveals a new, more efficient method; and leads to an extension that allows a permutation scheme to be applied to any Hadamard or simplex matrix in the appropriate equivalence class.

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18

Ikuta, Takuya, and Akihiro Munemasa. "Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4." Special Matrices 6, no. 1 (January 1, 2018): 1–10. http://dx.doi.org/10.1515/spma-2018-0001.

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Abstract We consider nonsymmetric hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of commutative nonsymmetric association schemes. First, we give a characterization of the eigenmatrix of a commutative nonsymmetric association scheme of class 3 whose Bose-Mesner algebra contains a nonsymmetric hermitian complex Hadamard matrix, and show that such a complex Hadamard matrix is necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.We also give nonsymmetric association schemes X of class 6 on Galois rings of characteristic 4, and classify hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of X. It is shown that such a matrix is again necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.

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19

Liu, Yiyu, Hanjie Liu, and Yuanguo Zhu. "An Approach for Numerical Solutions of Caputo–Hadamard Uncertain Fractional Differential Equations." Fractal and Fractional 6, no. 12 (November 23, 2022): 693. http://dx.doi.org/10.3390/fractalfract6120693.

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This paper is devoted to investigating a numerical scheme for solving the Caputo–Hadamard uncertain fractional differential equations (UFDEs) arising from nonlinear uncertain dynamic systems. In our approach, we define an α-path, which is a link between a Caputo–Hadamard UFDE and a Caputo–Hadamard fractional differential equation and is the inverse uncertainty distribution of a Caputo–Hadamard UFDE. Then, a formula for calculating the expected value of the Caputo–Hadamard UFDE is studied. With the help of the modified predictor–corrector method, some numerical algorithms for the inverse uncertainty distribution and the expected value of the solution of Caputo–Hadamard UFDEs are designed. Corresponding numerical examples are given to confirm the validity and accuracy of the proposed algorithms.

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20

Falcón, Raúl M., Víctor Álvarez, María Dolores Frau, Félix Gudiel, and María Belén Güemes. "Pseudococyclic Partial Hadamard Matrices over Latin Rectangles." Mathematics 9, no. 2 (January 6, 2021): 113. http://dx.doi.org/10.3390/math9020113.

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The classical design of cocyclic Hadamard matrices has recently been generalized by means of both the notions of the cocycle of Hadamard matrices over Latin rectangles and the pseudococycle of Hadamard matrices over quasigroups. This paper delves into this topic by introducing the concept of the pseudococycle of a partial Hadamard matrix over a Latin rectangle, whose fundamentals are comprehensively studied and illustrated.

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21

Matsuki, Norichika. "Circulant Hadamard matrices and Hermitian circulant complex Hadamard matrices." International Mathematical Forum 16, no. 1 (2021): 19–22. http://dx.doi.org/10.12988/imf.2021.912166.

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22

Zhang, Zhi, Wei Wei, and Jin Wang. "Generalization of Hermite-Hadamard inequalities involving Hadamard fractional integrals." Filomat 29, no. 7 (2015): 1515–24. http://dx.doi.org/10.2298/fil1507515z.

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In this paper, we firstly give a general integral identity for once differentiable mapping involving Hadamard fractional integrals. Secondly, we use this integral identity to derive some new generalization of fractional Hermite-Hadamard inequalities through GA-convex functions via power means and integrals GG-convex functions via power means. Some applications to special means of real numbers are given.

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23

Kotsireas, Ilias S., Christos Koukouvinos, and Jennifer Seberry. "Hadamard ideals and Hadamard matrices with two circulant cores." European Journal of Combinatorics 27, no. 5 (July 2006): 658–68. http://dx.doi.org/10.1016/j.ejc.2005.03.004.

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24

Đoković, Dragomir Ž., Oleg Golubitsky, and Ilias S. Kotsireas. "Some New Orders of Hadamard and Skew-Hadamard Matrices." Journal of Combinatorial Designs 22, no. 6 (June 12, 2013): 270–77. http://dx.doi.org/10.1002/jcd.21358.

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25

Farouk, Adda, and Qing-Wen Wang. "Construction of new Hadamard matrices using known Hadamard matrices." Filomat 36, no. 6 (2022): 2025–42. http://dx.doi.org/10.2298/fil2206025f.

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In this paper, by the use of Latin squares, we describe a procedure to construct Hadamard matrices using the existing Hadamard matrices of order m as input matrices. We propose constructions of Hadamard matrices of orders m(m ? 1), m(m/2 ? 1) and m(m/k ? 1), where k is a multiple of four that divides m into an even number. This work is a continuation of our previous one in [5].

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26

Bahmani Jafarloo, Iman, Cristiano Bocci, and Elena Guardo. "Hadamard Product of Monomial Ideals and the Hadamard Package." Mathematics 12, no. 7 (April 8, 2024): 1113. http://dx.doi.org/10.3390/math12071113.

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In this paper, we generalize and study the concept of Hadamard product of ideals of projective varieties to the case of monomial ideals. We have a research direction similar to the one of the join of monomial ideals contained in a paper of Sturmfels and Sullivant. In the second part of the paper, we give a brief tutorial on the Hadamard.m2 package of Macaulay2.

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27

Moslemipour, Ali, Mehdi Roohi, Mohammad Mardanbeigi, and Mahdi Azhini. "Monotone relations in Hadamard spaces." Filomat 33, no. 19 (2019): 6347–58. http://dx.doi.org/10.2298/fil1919347m.

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In this paper, the notion of W-property for subsets of X x X? is introduced and investigated, where X is an Hadamard space and X? is its linear dual space. It is shown that an Hadamard space X is flat if and only if X x X? has W-property. Moreover, the notion of monotone relation from an Hadamard space to its linear dual space is introduced. A characterization result for monotone relations with W-property (and hence in flat Hadamard spaces) is given. Finally, a type of Debrunner-Flor Lemma concerning extension of monotone relations in Hadamard spaces is proved.

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28

Matolcsi, Máté, Júlia Réffy, and Ferenc Szöllősi. "Constructions of Complex Hadamard Matrices via Tiling Abelian Groups." Open Systems & Information Dynamics 14, no. 03 (September 2007): 247–63. http://dx.doi.org/10.1007/s11080-007-9050-6.

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Applications in quantum information theory and quantum tomography have raised current interest in complex Hadamard matrices. In this note we investigate the connection between tiling of Abelian groups and constructions of complex Hadamard matrices. First, we recover a recent, very general construction of complex Hadamard matrices due to Dita [2] via a natural tiling construction. Then we find some necessary conditions for any given complex Hadamard matrix to be equivalent to a Dita-type matrix. Finally, using another tiling construction, due to Szabó [8], we arrive at new parametric families of complex Hadamard matrices of order 8, 12 and 16, and we use our necessary conditions to prove that these families do not arise with Dita's construction. These new families complement the recent catalogue [10] of complex Hadamard matrices of small order.

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29

WANG, BIN, WENLONG JI, LEGUI ZHANG, and XUAN LI. "THE RELATIONSHIP BETWEEN FRACTAL DIMENSIONS OF BESICOVITCH FUNCTION AND THE ORDER OF HADAMARD FRACTIONAL INTEGRAL." Fractals 28, no. 07 (November 2020): 2050128. http://dx.doi.org/10.1142/s0218348x20501285.

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In this paper, we mainly research on Hadamard fractional integral of Besicovitch function. A series of propositions of Hadamard fractional integral of [Formula: see text] have been proved first. Then, we give some fractal dimensions of Hadamard fractional integral of Besicovitch function including Box dimension, [Formula: see text]-dimension and Packing dimension. Finally, relationship between the order of Hadamard fractional integral and fractal dimensions of Besicovitch function has also been given.

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30

Białas, Stanisław, and Michał Góra. "On the Existence of Hurwitz Polynomials with no Hadamard Factorization." Electronic Journal of Linear Algebra 36, no. 36 (April 14, 2020): 210–13. http://dx.doi.org/10.13001/ela.2020.5097.

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A Hurwitz stable polynomial of degree $n\geq1$ has a Hadamard factorization if it is a Hadamard product (i.e., element-wise multiplication) of two Hurwitz stable polynomials of degree $n$. It is known that Hurwitz stable polynomials of degrees less than four have a Hadamard factorization. It is shown that, for arbitrary $n\geq4$, there exists a Hurwitz stable polynomial of degree $n$ which does not have a Hadamard factorization.

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31

BENJAMIN, A. PETER. "Hadamard Product of a Class of Holomorphic Functions with an Arbitrary Fixed Point." Journal of Applied Science, Information and Computing 3, no. 1 (July 20, 2022): 54–70. http://dx.doi.org/10.59568/jasic-2022-3-1-07.

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Hadamard product of holomorphic function is simply entry wise multiplication of two functions f and g in . The Hadamard products of two functions have one thing in common that is, it involves the origin. Irrespective of the factors of the Hadamard product either power series or holomorphic functions, the open sets on which they are examined contain the origin. The aim of this study, therefore, is to investigate on the properties of Hadamard product for a class of holomorphic functions with an arbitrary fixed point. The concept of Hadamard product, Cauchy-Schwartz, holomorphic functions, Ruscheweyh differential operators, and Nevanlinna’s theorem are employed in this study. This study generalized the coefficient inequalities for starlike and convex functions of exponential order  with an arbitrary fixed point using Ruscheweyh derivative. This study further provides an additional inequality and Hadamard product for a class of holomorphic functions with an arbitrary fixed point. It is concluded that Ruscheweyh derivative is an effective tool in the generalization of Hadamard product for a class of holomorphic functions with an arbitrary fixed point.

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32

Christou, Dimitrios, Marilena Mitrouli, and Jennifer Seberry. "Embedding and Extension Properties of Hadamard Matrices Revisited." Special Matrices 6, no. 1 (March 1, 2018): 155–65. http://dx.doi.org/10.1515/spma-2018-0012.

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Abstract Hadamard matrices have many applications in several mathematical areas due to their special form and the numerous properties that characterize them. Based on a recently developed relation between minors of Hadamard matrices and using tools from calculus and elementary number theory, this work highlights a direct way to investigate the conditions under which an Hadamard matrix of order n − k can or cannot be embedded in an Hadamard matrix of order n. The results obtained also provide answers to the problem of determining the values of the spectrum of the determinant function for specific orders of minors of Hadamard matrices by introducing an analytic formula.

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33

Farouk, Adda, and Qing-Wen Wang. "An infinite family of Hadamard matrices constructed from Paley type matrices." Filomat 34, no. 3 (2020): 815–34. http://dx.doi.org/10.2298/fil2003815f.

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An n x n matrix whose entries are from the set {1,-1} is called a Hadamard matrix if HH? = nIn. The Hadamard conjecture states that if n is a multiple of four then there always exists Hadamard matrices of this order. But their construction remain unknown for many orders. In this paper we construct Hadamard matrices of order 2q(q + 1) from known Hadamard matrices of order 2(q + 1), where q is a power of a prime number congruent to 1 modulo 4. We show then two ways to construct them. This work is a continuation of U. Scarpis? in [7] and Dragomir-Z. Dokovic?s in [10].

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34

Mehmood, Sajid, and Ghulam Farid. "Fractional Hadamard and Fejer-Hadamard inequalities for exponentially m-convex function." Studia Universitatis Babes-Bolyai Matematica 66, no. 4 (December 13, 2021): 629–40. http://dx.doi.org/10.24193/subbmath.2021.4.03.

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Fractional integral operators play a vital role in the advancement of mathematical inequalities. The aim of this paper is to present the Hadamard and the Fej er-Hadamard inequalities for generalized fractional integral operators con- taining Mittag-Le er function. Exponentially m-convexity is utilized to establish these inequalities. By xing parameters involved in the Mittag-Le er function Hadamard and the Fej er-Hadamard inequalities for various well known fractional integral operators can be obtained.

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35

Butt, Saad Ihsan, Saba Yousaf, Khuram Ali Khan, Rostin Matendo Mabela, and Abdullah M. Alsharif. "Fejér–Pachpatte–Mercer-Type Inequalities for Harmonically Convex Functions Involving Exponential Function in Kernel." Mathematical Problems in Engineering 2022 (March 2, 2022): 1–19. http://dx.doi.org/10.1155/2022/7269033.

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In the present study, fractional variants of Hermite–Hadamard, Hermite–Hadamard–Fejér, and Pachpatte inequalities are studied by employing Mercer concept. Firstly, new Hermite–Hadamard–Mercer-type inequalities are presented for harmonically convex functions involving fractional integral operators with exponential kernel. Then, weighted Hadamard–Fejér–Mercer-type inequalities involving exponential function as kernel are proved. Finally, Pachpatte–Mercer-type inequalities for products of harmonically convex functions via fractional integral operators with exponential kernel are constructed.

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36

Guo, Shuya, Yu-Ming Chu, Ghulam Farid, Sajid Mehmood, and Waqas Nazeer. "Fractional Hadamard and Fejér-Hadamard Inequalities Associated with Exponentially s,m-Convex Functions." Journal of Function Spaces 2020 (August 7, 2020): 1–10. http://dx.doi.org/10.1155/2020/2410385.

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The aim of this paper is to present the fractional Hadamard and Fejér-Hadamard inequalities for exponentially s,m-convex functions. To establish these inequalities, we will utilize generalized fractional integral operators containing the Mittag-Leffler function in their kernels via a monotone function. The presented results in particular contain a number of fractional Hadamard and Fejér-Hadamard inequalities for s-convex, m-convex, s,m-convex, exponentially convex, exponentially s-convex, and convex functions.

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37

ASAHI, Hideyasu. "A Function Generator for Walsh Order Hadamard Matrix and Fast Walsh-Hadamard Transform." Geoinformatics 11, no. 1 (2000): 3–9. http://dx.doi.org/10.6010/geoinformatics1990.11.1_3.

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38

NIKONOV, VLADIMIR, and SERGEY KONONOV. "ABOUT SOME PROPERTIES OF QUASI-HADAMARD MATRICES DEFINING BIJECTIVE TRANSFORMATIONS." Computational Nanotechnology 9, no. 1 (March 28, 2022): 32–38. http://dx.doi.org/10.33693/2313-223x-2022-9-1-32-38.

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The article continues studies of bijective mapping determined by quasi-hadamard matrices started in work. It is proved that for different quasi-hadamard martices there are different mappings. All quasi-hadamard matrices of orders 4 and 8 are also described.

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39

Huang, Hui, Kaihong Zhao, and Xiuduo Liu. "On solvability of BVP for a coupled Hadamard fractional systems involving fractional derivative impulses." AIMS Mathematics 7, no. 10 (2022): 19221–36. http://dx.doi.org/10.3934/math.20221055.

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<abstract><p>Hadamard fractional calculus is one of the most important fractional calculus theories. Compared with a single Hadamard fractional order equation, Hadamard fractional differential equations have a more complex structure and a wide range of applications. It is difficult and challenging to study the dynamic behavior of Hadamard fractional differential equations. This manuscript mainly deals with the boundary value problem (BVP) of a nonlinear coupled Hadamard fractional system involving fractional derivative impulses. By applying nonlinear alternative of Leray-Schauder, we find some new conditions for the existence of solutions to this nonlinear coupled Hadamard fractional system. Our findings reveal that the impulsive function and its impulsive point have a great influence on the existence of the solution. As an application, we discuss an interesting example to verify the correctness and validity of our results.</p></abstract>

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40

Nonlaopon, Kamsing, Ghulam Farid, Ammara Nosheen, Muhammad Yussouf, and Ebenezer Bonyah. "New Generalized Riemann–Liouville Fractional Integral Versions of Hadamard and Fejér–Hadamard Inequalities." Journal of Mathematics 2022 (April 26, 2022): 1–17. http://dx.doi.org/10.1155/2022/8173785.

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In this paper, a new class of functions, namely, exponentially α , h − m − p -convex functions is introduced to unify various classes of functions already defined in the subject of convex analysis. By using this class of functions, generalized versions of well known fractional integral inequalities of Hadamard and Fejér–Hadamard type are obtained. The results of this paper generate fractional integral inequalities of Hadamard and Fejér–Hadamard type for various types of convex and exponentially convex functions simultaneously.

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Nonlaopon, Kamsing, Ghulam Farid, Ammara Nosheen, Muhammad Yussouf, and Ebenezer Bonyah. "New Generalized Riemann–Liouville Fractional Integral Versions of Hadamard and Fejér–Hadamard Inequalities." Journal of Mathematics 2022 (April 26, 2022): 1–17. http://dx.doi.org/10.1155/2022/8173785.

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In this paper, a new class of functions, namely, exponentially α , h − m − p -convex functions is introduced to unify various classes of functions already defined in the subject of convex analysis. By using this class of functions, generalized versions of well known fractional integral inequalities of Hadamard and Fejér–Hadamard type are obtained. The results of this paper generate fractional integral inequalities of Hadamard and Fejér–Hadamard type for various types of convex and exponentially convex functions simultaneously.

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42

GULSHAN, GHAZALA, RASHIDA HUSSAIN, and ASGHAR ALI. "POST QUANTUM-HERMITE-HADAMARD INEQUALITIES FOR DIFFERENTIABLE CONVEX FUNCTIONS WITH A CRITICAL POINT." Journal of Science and Arts 21, no. 2 (June 30, 2021): 337–46. http://dx.doi.org/10.46939/j.sci.arts-21.2-a02.

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In this study, we obtained some new post quantum-Hermite-Hadamard inequalities for differentiable convex function with critical point by using generalized (p, q)- Hermite-Hadamard Inequality. The perseverance of this article is to establish different results on the left-hand side of (p,q)-Hermite-Hadamard inequality for differentiable convex function along with critical point. Special cases were obtained for different (p, q)-Hermite Hadamard inequalies with the critical point c for some special values of q.

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43

Deveci, Ömür, ‪Yeşim Aküzüm, and Muhammad Eshaq Rashedi. "The Hadamard-type k-step Pell sequences." Notes on Number Theory and Discrete Mathematics 28, no. 2 (June 10, 2022): 339–49. http://dx.doi.org/10.7546/nntdm.2022.28.2.339-349.

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In this paper, we define the Hadamard-type k-step Pell sequence by using the Hadamard-type product of characteristic polynomials of the Pell sequence and the k-step Pell sequence. Also, we derive the generating matrices for these sequences, and then we obtain relationships between the Hadamard-type k-step Pell sequences and these generating matrices. Furthermore, we produce the Binet formula for the Hadamard-type k-step Pell numbers for the case that k is odd integers and k ≥ 3. Finally, we derive some properties of the Hadamard-type k-step Pell sequences such as the combinatorial representation, the generating function, and the exponential representation by using its generating matrix.

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Faisal, Shah, Muhammad Khan, and Sajid Iqbal. "Generalized Hermite-Hadamard-Mercer type inequalities via majorization." Filomat 36, no. 2 (2022): 469–83. http://dx.doi.org/10.2298/fil2202469f.

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The Hermite-Hadamard inequality has been recognized as the most pivotal inequality which has grabbed the attention of several mathematicians. In recent years, load of results have been established for this inequality. The main theme of this article is to present generalized Hermite-Hadamard inequality via the Jensen-Mercer inequality and majorization concept. We establish a Hermite-Hadamard inequality of the Jensen-Mercer type for majorized tuples. With the aid of weighted generalized Mercer?s inequality, we also prove a weighted generalized Hermite-Hadamard inequality for certain tuples. The idea of obtaining the results of this paper, may explore a new way for derivation of several other results for Hermite-Hadamard inequality.

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Giles, J. R., and Scott Sciffer. "On weak Hadamard differentiability of convex functions on Banach spaces." Bulletin of the Australian Mathematical Society 54, no. 1 (August 1996): 155–66. http://dx.doi.org/10.1017/s000497270001515x.

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We study two variants of weak Hadamard differentiability of continuous convex functions on a Banach space, uniform weak Hadamard differentiability and weak Hadamard directional differentiability, and determine their special properties on Banach spaces which do not contain a subspace topologically isomorphic to l1.

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Rashid, Saima, Muhammad Aslam Noor, and Khalida Inayat Noor. "Inequalities Pertaining Fractional Approach through Exponentially Convex Functions." Fractal and Fractional 3, no. 3 (June 27, 2019): 37. http://dx.doi.org/10.3390/fractalfract3030037.

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In this article, certain Hermite-Hadamard-type inequalities are proven for an exponentially-convex function via Riemann-Liouville fractional integrals that generalize Hermite-Hadamard-type inequalities. These results have some relationships with the Hermite-Hadamard-type inequalities and related inequalities via Riemann-Liouville fractional integrals.

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Stoenchev, Miroslav, Venelin Todorov, and Slavi Georgiev. "Notes on the Overconvergence of Fourier Series and Hadamard–Ostrowski Gaps." Mathematics 12, no. 7 (March 25, 2024): 979. http://dx.doi.org/10.3390/math12070979.

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This paper examines the relationship between the overconvergence of Fourier series and the existence of Hadamard–Ostrowski gaps. Ostrowski’s result on the overconvergence of power series serves as a motivating factor for obtaining a natural generalization: the overconvergence of Fourier series. The connection between Hadamard–Ostrowski gaps and the overconvergence of Fourier series is clarified by applying the Hadamard three-circle theorem and the theory of orthogonal polynomials. Our main result is obtained by applying the Hadamard three-circle theorem.

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Yamada, Mieko. "Some new series of Hadamard matrices." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 46, no. 3 (June 1989): 371–83. http://dx.doi.org/10.1017/s144678870003086x.

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AbstractThe purpose of this paper is to prove (1) if q ≡ 1 (mod 8) is a prime power and there exists a Hadamard matrix of order (q − 1)/2, then we can construct a Hadamard matrix of order 4q, (2) if q ≡ 5 (mod 8) is a prime power and there exists a skew-Hadamard matrix of order (q + 3)/2, then we can construct a Hadamard matrix of order 4(q + 2), (3) if q ≡ 1 (mod 8) is a prime power and there exists a symmetric C-matrix of order (q + 3)/2, then we can construct a Hadamard matrix of order 4(q + 2).We have 36, 36 and 8 new orders 4n for n ≤ 10000, of Hadamard matrices from the first, the second and third theorem respectively, which were known to the list of Geramita and Seberry. We prove these theorems by using an adaptation of generalized quaternion type array and relative Gauss sums.

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Samanta, Supriti, Goutam K. Maity, and Subhadipta Mukhopadhyay. "Implementation of Orthogonal Codes Using MZI." Micro and Nanosystems 12, no. 3 (December 1, 2020): 159–67. http://dx.doi.org/10.2174/1876402912666200211121624.

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Background: In Code Division Multiple Access (CDMA)/Multi-Carrier CDMA (MCCDMA), Walsh-Hadamard codes are widely used for its orthogonal characteristics, and hence, it leads to good contextual connection property. These orthogonal codes are important because of their various significant applications. Objective: To use the Mach–Zehnder Interferometer (MZI) for all-optical Walsh-Hadamard codes is implemented in this present paper. Method: The Mach–Zehnder Interferometer (MZI) is considered for the Tree architecture of Semiconductor Optical Amplifier (SOA). The second-ordered Hadamard and the inverse Hadamard matrix are constructed using SOA-MZIs. Higher-order Hadamard matrix (H4) formed by the process of Kronecker product with lower-order Hadamard matrix (H2) is also analyzed and constructed. Results: To experimentally get the result from these schemes, some design issues e,g Time delay, nonlinear phase modulation, extinction ratio, and synchronization of signals are the important issues. Lasers of wavelength 1552 nm and 1534 nm can be used as input and control signals, respectively. As the whole system is digital, intensity losses due to couplers in the interconnecting stage may not create many problems in producing the desired optical bits at the output. The simulation results were obtained by Matlab-9. Here, Hadamard H2 (2×2) matrix output beam intensity (I ≈ 108 w.m-2) for different values of inputs. Conclusion: Implementation of Walsh-Hadamard codes using MZI is explored in this paper, and experimental results show the better performance of the proposed scheme compared to recently reported methods using electronic circuits regarding the issues of versatility, reconfigurability, and compactness. The design can be used and extended for diverse applications for which Walsh-Hadamard codes are required.

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Park, Ju Yong, Moon Ho Lee, and Wei Duan. "The New Block Circulant Hadamard Matrices." Journal of the Institute of Electronics and Information Engineers 51, no. 5 (May 25, 2014): 3–10. http://dx.doi.org/10.5573/ieie.2014.51.5.003.

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