The space of directed sets is a Banach space in which convex compact subsets of Rn are embedded. Each directed set is visualized as a (nonconvex) subset of Rn, which is comprised of a convex, a concave and a mixed-type part. Following an idea of A. Rubinov, the directed subdifferential of a difference of convex (DC) functions is defined as the directed difference of the corresponding embedded c...

The characterization of Hadamard states in terms of a specific form of the wavefront set of their two-point functions has been developed some years ago by Radzikowski for scalar fields on a four-dimensional globally hyperbolic spacetime, and initiated a major progress in the understanding of Hadamard states and the further development of quantum field theory in curved spacetime. In the present ...

In this article, we provide new methods to look for lightweight MDS matrices, and in particular involutory ones. By proving many new properties and equivalence classes for various MDS matrices constructions such as circulant, Hadamard, Cauchy and Hadamard-Cauchy, we exhibit new search algorithms that greatly reduce the search space and make lightweight MDS matrices of rather high dimension poss...

Introduction: A reduced field-of-view (FOV) single-shot EPI (ss-EPI) method that uses a 2D echoplanar RF (2D-EPRF) excitation has recently been proposed for high-resolution DWI [1]. This method takes advantage of ss-EPI’s robustness against motion during diffusion encoding gradients. Furthermore, it allows for contiguous multi-slice imaging without the need for slice skip. However, there is a l...

ABSTRACT: In this paper, a complete construction of quaternary complex Hadamard matrices of order 2 n is obtained using the method of Sylvester construction and Williamson construction. Williamson construction has been generalized to obtain any kind of Hadamard matrices (Complex or Real Numbers). Non-equivalent family of Hadamard Matrices can be obtained using the Generalized Williamson constru...

Abstract. In this paper we define and verify a subclass of harmonic univalent functions involving the argument of complex-value functions of the form f = h + ¯g and investigate some properties of this subclass e.g. necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.Abstract. In this paper we define and verify a subclass of harmonic univalent func...

Weifeng Su and Xiang-Gen Xia. 2003. "On Space-Time Block Codes from Complex Orthogonal Designs", Wireless Personal Communications 25: 1–26. A. V. Geramita and J. Seberry. 1979. Orthogonal Designs, Quadratic Forms and Hadamard Matrices. Lecture Notes in Pure and Applied Mathematics, Vol. 43, Marcel Dekker: New York and Basel. V. Tarokh, H. Jafarkhani and A. R. Calderbank. 1999. "S...

We examine the relationship between three approaches (Hadamard, DeWitt-Schwinger and adiabatic) to renormalization of expectation values field operators acting on a charged quantum scalar field. First, we demonstrate that representation Feynman Green's function is particular case Hadamard representation. Next, restrict attention spatially flat Friedmann-Lemaitre-Robertson-Walker universe with t...

Abstract In this study, we use the fuzzy order relation to show some novel variants of Hermite–Hadamard inequalities for pre-invex fuzzy-interval-valued mappings ( F-I∙V-Ms ), which term fuzzy-interval and Hermite–Hadamard–Fejér inequalities. This is defined as level space by Kulisch–Miranker relation. There are also new exceptional instances mentioned. The theory proposed in research shown wit...

A Z2Z4-linear Hadamard code of length α + 2β = 2 t is a binary Hadamard code which is the Gray map image of a Z2Z4-additive code with α binary coordinates and β quaternary coordinates. It is known that there are exactly b t−1 2 c and b t 2c nonequivalent Z2Z4-linear Hadamard codes of length 2t, with α = 0 and α 6= 0, respectively, for all t ≥ 3. In this paper, it is shown that each Z2Z4-linear ...