Search Results (147)

In Algebraic Statistics, M.A. Cueto, J. Morton and B. Sturmfels introduced a statistical model, the Restricted Boltzmann Machine, which introduced the Hadamard product of two or more vectors of an affine or projective space, i.e., the componentwise product of their entries, forcing Algebraic Geometry to enter. The Hadamard product $X\star Y$ of two subvarieties $X,Y\subset {\mathbb{P}}^n$ is defined as the Zariski closure of the Hadamard product of its elements. Recently, D. Antolini and A. Oneto introduced and studied the definition of Hadamard rank, and we prove some results on it. Moreover, we prove some theorems on the dimension and shape of the Hadamard powers of X. The aim is to describe the images of the Hadamard products without taking the Zariski closure. We also discuss several scenarios describing the case in which some of the data, i.e., the variety X, is wrong or it is not possible to recover it. Full article

We present hybrid quantum–classical algorithms to compute time-dependent Møller wavepacket correlation functions via digital quantum simulation. Reactant and product channel wavepackets are encoded as qubit states, evolved under a discretized molecular Hamiltonian, and their correlation is reconstructed using both a modified Hadamard test and a multi-fidelity estimation (MFE) protocol. The method is applied to the collinear H + H₂ exchange reaction on a London–Eyring–Polanyi–Sato potential energy surface. Quantum-estimated correlation functions show quantitative agreement with high-resolution classical wavepacket simulations across the full time domain, reproducing both short-time scattering peaks and long-time oscillatory dynamics. The ancilla-free MFE protocol achieves matching results with reduced circuit depth. These results provide a proof of principle that digital quantum circuits can be used to accurately calculate the wavepacket correlation functions for a benchmark chemical reaction system. Full article

This paper explains why the critical line sits at the real part equal to one-half by treating it as an intrinsic boundary of a reparametrized complex plane (“$z$-space”), not a mere artifact of functional symmetry. In $z$-space the real part is defined by a geometric-series map that gives rise to a rulebook for admissible analytic operations. Within this setting we rederive the classical toolkit—the eta–zeta relation, Gamma reflection and duplication, theta–Mellin identity, functional equation, and the completed zeta—without importing analytic continuation from the usual $s$-variable. We show that access to the left half-plane occurs entirely through formulas written on the right, with boundary matching only along the line with the real part equal to one-half. A global Hadamard product confirms the consistency and fixed location of this boundary, and a holomorphic change of variables transports these conclusions into the classical setting. Full article

This paper presents new subclasses of multivalent analytic functions defined through the $\mathfrak{q}$-derivative operator and examines their inclusion properties. By employing the Jackson $\mathfrak{q}$-derivative, we construct generalized operators that encompass numerous previously established operators and provide a framework for defining new classes with distinctive analytic features. Our main results are derived using techniques from differential subordination theory for complex-valued functions of one variable. Some applications of Bernardi operator are discussed. Full article

The findings of this study are connected with geometric function theory and were acquired using subordination-based techniques in conjunction with the Hurwitz–Lerch Zeta function. We used the Hurwitz–Lerch Zeta function to investigate certain properties of multivalent meromorphic functions. The primary objective of this study is to provide an investigation on the argument properties of multivalent meromorphic functions in a punctured open unit disc and to obtain some results for its subclass. Full article

Technological decoupling, geopolitical tensions, and carbon neutrality pressures have created systemic risks, making supply chain security a global concern. Digital-driven new quality productivity (NQP), as a key driver of supply chain upgrading, plays a crucial role in restructuring modern supply chain systems and enhancing resilience. Based on data from Chinese supply chain data from listed companies (2012–2023), this study integrates enterprise-level NQP and applies complex network methods and the Hadamard product model to analyze how NQP regulates supply chain resilience. The results show that NQP affects network resilience through three nonlinear coupling mechanisms: strengthening defense at fixed points, promoting recovery through chain reinforcement, and enhancing sustainability via network expansion. Its impact is stage-dependent—showing partial vulnerability during early technology diffusion but significantly improving overall resilience at maturity, with structural imbalance remaining a potential risk. This study provides theoretical and practical insights for optimizing supply chain structures and improving risk prevention and collaborative capabilities. Full article

This study examines the necessary requirements for some analytic function subclasses, especially those associated with the generalized Mittag-Leffler function, to be classified as univalent function subclasses that are determined by particular geometric constraints. The core methodology revolves around the application of the Hadamard (or convolution) product involving a normalized Mittag-Leffler function ${\mathbb{M}}_{\kappa ,\chi }\left(\zeta \right)$, leading to the definition of a new linear operator ${\mathfrak{S}}_{\chi ,\vartheta }^{\kappa }\hslash \left(\zeta \right).$ We investigate inclusion results in the recently defined subclasses $\tilde{\mathsf{\Xi }}(\varpi ,\varrho ),\widehat{\mathfrak{L}}(\varpi ,\varrho ),\widehat{\mathfrak{K}}(\varpi ,\varrho )$ and $\widehat{\mathfrak{F}}(\varpi ,\varrho )$, which generalize the classical classes of starlike, convex, and close-to-convex functions. This is achieved by utilizing recent developments in the theory of univalent functions. In addition, we examine the behavior of functions from the class ${\mathfrak{R}}_{\theta }(E,V)$ under the action of the convolution operator ${\mathbb{W}}_{\chi ,\vartheta }^{\kappa }h\left(\zeta \right)$, establishing sufficient criteria for the resulting images to lie within the subclasses of analytic function. Also, certain mapping properties related to these subclasses are analyzed. In addition, the geometric features of an integral operator connected to the Mittag-Leffler function are examined. A few particular cases of our main findings are also mentioned and examined and the paper ends with the conclusions regarding the obtained results. Full article

This paper introduces a novel generalized q-symmetric differential operator for studying a certain subclass of univalent functions with negative coefficients. We establish several significant theoretical results for this class, including sharp coefficient bounds and characterization theorems based on the generalized Hadamard product. Two significant applications demonstrate the theoretical framework’s practical utility. First, in the context of geometric modeling, we demonstrate how the function class and operator can be utilized to create and control complex, non-overlapping transformations. Second, in digital signal processing, we show that these functions serve as stable digital filter prototypes and that our operator is an effective tool for fine-tuning the filter’s frequency response. These applications bridge the gap between abstract geometric function theory and practical system design by demonstrating the operator’s versatility as a tool for analysis and synthesis. Full article

In this paper, we integrate the concepts of spiral-like functions and Janowski-type functions within the framework of q-calculus to define new subclasses in the open unit disk. Our primary focus is on analyzing convolution conditions that form the foundation for further theoretical developments. The main contributions include establishing sufficient conditions and applying Robertson’s theorem. Furthermore, motivated by a recent definition, we propose analogous neighborhood concepts for the above-mentioned classes, and we explore the corresponding neighborhood results. Full article

Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by developing an explicit quantum algorithm that implements the time evolution of a second-order time-discretized version of the Lorenz model. The Lorenz model is a celebrated system of nonlinear ordinary differential equations that has been extensively studied in the contexts of climate science, fluid dynamics, and chaos theory. Our algorithm possesses a recursive structure and requires only a linear number of copies of the initial state with respect to the number of integration time-steps. This provides a significant improvement over previous approaches, while preserving the characteristic quantum speed-up in terms of the dimensionality of the underlying differential equations system, which similar time-marching quantum algorithms have previously demonstrated. Notably, by classically implementing the proposed algorithm, we showcase that it accurately captures the structural characteristics of the Lorenz system, reproducing both regular attractors–limit cycles–and the chaotic attractor within the chosen parameter regime. Full article

The accurate identification of seismic faults, which serve as crucial fluid migration pathways in hydrocarbon reservoirs, is of paramount importance for reservoir characterization. Traditional interpretation is inefficient. It also struggles with complex geometries, failing to meet the current exploration demands. Deep learning boosts fault identification significantly but struggles with edge accuracy and noise robustness. To overcome these limitations, this research introduces SwiftSeis-AWNet, a novel lightweight and high-precision network. The network is based on an optimized MedNeXt architecture for better fault edge detection. To address the noise from simple feature fusion, a Semantics and Detail Infusion (SDI) module is integrated. Since the Hadamard product in SDI can cause information loss, we engineer an Attention-Weighted Semantics and Detail Infusion (AWSDI) module that uses dynamic multi-scale feature fusion to preserve details. Validation on field seismic datasets from the Netherlands F3 and New Zealand Kerry blocks shows that SwiftSeis-AWNet mitigates challenges like the loss of small-scale fault features and misidentification of fault intersection zones, enhancing the accuracy and geological reliability of automated fault identification. Full article

Traditional antenna arrays for direction-of-arrival (DOA) estimation typically require numerous elements to achieve target performance, increasing system complexity and cost. Reconfigurable intelligent surfaces (RISs) offer a promising alternative, yet their performance critically depends on phase coding design. To address this, we propose a phase coding design method for RIS-aided DOA estimation with a single receiving channel. First, we establish a system model where averaged received signals construct a power-based formulation. This transforms DOA estimation into a compressed sensing-based sparse recovery problem, with the RIS far-field power radiation pattern serving as the measurement matrix. Then, we derive the decoupled expression of the measurement matrix, which consists of the phase coding matrix, propagation phase shifts, and array steering matrix. The phase coding design is then formulated as a Frobenius norm minimization problem, approximating the Gram matrix of the equivalent measurement matrix to an identity matrix. Accordingly, the phase coding design problem is reformulated as a Frobenius norm minimization problem, where the Gram matrix of the equivalent measurement matrix is approximated to an identity matrix. The phase coding is deterministically constructed as the product of a unitary matrix and a partial Hadamard matrix. Simulations demonstrate that the proposed phase coding design outperforms random phase coding in terms of angular estimation accuracy, resolution probability, and the requirement of coding sequences. Full article

The study of various subclasses of univalent functions involving the solutions to various differential equations is not totally new, but studies of analytic functions with respect to $(\mathsf{\ell },\kappa )$-symmetric points are rarely conducted. Here, using a differential operator which was defined using the Hadamard product of Mittag–Leffler function and general analytic function, we introduce a new class of starlike functions with respect to $(\mathsf{\ell },\kappa )$-symmetric points associated with the vertical domain. To define the function class, we use a Carathéodory function which was recently introduced to study the impact of various conic regions on the vertical domain. We obtain several results concerned with integral representations and coefficient inequalities for functions belonging to this class. The results obtained by us here not only unify the recent studies associated with the vertical domain but also provide essential improvements of the corresponding results. Full article

The direct porting of the Range Migration Algorithm to GPUs for three-dimensional (3D) cylindrical synthetic aperture radar (CSAR) imaging faces difficulties in achieving real-time performance while the architecture and programming models of GPUs significantly differ from CPUs. This paper proposes a GPU-optimized implementation for accelerating CSAR imaging. The proposed method first exploits the concentric-square-grid (CSG) interpolation to reduce the computational complexity for reconstructing a uniform 2D wave-number domain. Although the CSG method transforms the 2D traversal interpolation into two independent 1D interpolations, the interval search to determine the position intervals for interpolation results in a substantial computational burden. Therefore, binary search is applied to avoid traditional point-to-point matching for efficiency improvement. Additionally, leveraging the partition independence of the grid distribution of CSG, the 360° data are divided into four streams along the diagonal for parallel processing. Furthermore, high-speed shared memory is utilized instead of high-latency global memory in the Hadamard product for the phase compensation stage. The experimental results demonstrate that the proposed method achieves CSAR imaging on a $1440\times 100\times 128$ dataset in 0.794 s, with an acceleration ratio of 35.09 compared to the CPU implementation and 5.97 compared to the conventional GPU implementation. Full article

Existing studies on ontology evolution lack automated mechanisms to balance semantic coherence and adaptability under real-time uncertainties, particularly in resolving spatiotemporal asymmetry and multidimensional coupling imbalances in dam-break scenarios. Traditional methods such as WordNet’s tree symmetry and FrameNet’s frame symmetry fail to formalize dynamic adjustments through quantitative metrics, leading to path dependency and delayed responses. This study addresses this gap by introducing a novel symmetry-entropy-constrained matrix fusion algorithm, which integrates algebraic direct sum operations and Hadamard product with entropy-driven adaptive weighting. The original contribution lies in the symmetry entropy metric, which quantifies structural deviations during fusion to systematically balance semantic stability and adaptability. This work formalizes ontology evolution as a symmetry-driven optimization process. Experimental results demonstrate that shared concepts between ontologies (s = 3) reduce structural asymmetry by 25% compared to ontologies (s = 1), while case studies validate the algorithm’s ability to reconcile discrepancies between theoretical models and practical challenges in evacuation efficiency and crowd dynamics. This advancement promotes the evolution of traditional emergency management systems towards an adaptive intelligent form. Full article