In this work we study the issue of geodesic extendibility on complete and locally compact metric length spaces. We focus geometric structure space $(\Sigma (X),d_H)$ balls endowed with Hausdorff distance give an explicit isometry between closed half-space $ X\times \mathbb{R}_{\ge 0}$ a taxicab metric. Among applications establish group $\mbox{Iso} (X,d)$ (\Sigma when $(X,d)$ is Hadamard space.

The new neural network classifier we propose transforms the classification problem into the coding theory problem of decoding a noisy codeword. An input vector in the feature space is transformed into an internal representation which is a codeword in the code space, and then error correction decoded in this space to classify the input feature vector to its class. Two classes of codes which give...

‎This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$‎. ‎Some applications to these inequalities are also given‎. ‎In addi...

We define several operations that switch substructures of Hadamard matrices thereby producing new, generally inequivalent, Hadamard matrices. These operations have application to the enumeration and classification of Hadamard matrices. To illustrate their power, we use them to greatly improve the lower bounds on the number of equivalence classes of Hadamard matrices in orders 32 and 36 to 3,578...

In this paper we study a one-dimensional quantum random walk with the Hadamard transformation which is often called the Hadamard walk. We construct the Hadamard walk using a transition matrix on probability amplitude and give some results on symmetry of probability distributions for the Hadamard walk.

We demonstrate how to efficiently implement extremely high-dimensional compressive imaging of a bi-photon probability distribution. Our method uses fast-Hadamard-transform Kronecker-based compressive sensing to acquire the joint space distribution. We list, in detail, the operations necessary to enable fast-transform-based matrix-vector operations in the joint space to reconstruct a 16.8 millio...

In this work, we investigate the asymptotic stability of zero solution for Caputo-Hadamard fractional dynamic equations on a time scale. We will make use Krasnoselskii fixed point theorem in weighted Banach space to show new results.

Spin models for link invariants were introduced by Jones [7], and their connection to combinatorics was revealed first in [4]. Jaeger and Nomura [6] constructed nonsymmetric spin models for link invariants from Hadamard matrices, and showed that these models give link invariants which depend nontrivially on link orientation. These models are a modification of the Hadamard model originally const...

In this paper, the fast algorithm to Walsh-Hadamard transform (WHT) is studied from the point of view of the optical computation. Firstly, MSD addition and butterfly calculation in discrete WHT are presented in detail. Then the design and implementation scheme of fast algorithm of WHT is proposed and the software simulations to fast WHT are carried out optically. Meanwhile, the computational co...

The precoding scheme based on real Hadamard transform is an effective and flexible way for reducing the peak-to-average power ratio (PAPR) of OFDM signals. However, the reduction capacity of PAPR is limited for real Hadamard transform method. In this paper, the new scheme based on complex Hadamard transform is proposed. The simulation results indicate that the proposed scheme may obtain a 1.2 d...