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In this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis.

We introduce and investigate the complex space HC consisting of all 2 × 2 complex matrices of the form ξ=z1+iw1z2+iw2−z‾2−iw‾2z‾1+iw‾1, (z1,w1,z2,w2)∈C4.

We develop on HC a new matrix holomorphic structure for which we provide the fundamental operational calculus properties.

We give sufficient and necessary conditions in terms of Cauchy–Riemann type quaternionic differential equations for holomorphicity of a function of one complex matrix variable ξ∈HC. In particular, we show that we have a lot of holomorphic functions of one matrix quaternion variable.

We are interested in modeling the impact of spatial and interindustry dependence on firm-level innovation of Chinese firms The existence of network ties between cities imply that changes taking place in one city could influence innovation by firms in nearby cities (local spatial spillovers), or set in motion a series of spatial diffusion and feedback impacts across multiple cities (global spatial spillovers). We use the term local spatial spillovers to reflect a scenario where only immediately neighboring cities are impacted, whereas the term global spatial spillovers represent a situation where impacts fall on neighboring cities, as well as higher order neighbors (neighbors to the neighboring cities, neighbors to the neighbors of the neighbors, and so on). Global spatial spillovers also involve feedback impacts from neighboring cities, and imply the existence of a wider diffusion of impacts over space (higher order neighbors).

Similarly, the existence of national interindustry input-output ties implies that changes occurring in one industry could influence innovation by firms operating in directly related industries (local interindustry spillovers), or set in motion a series of in interindustry diffusion and feedback impacts across multiple industries (global interindustry spillovers).

Typical linear models of firm-level innovation based on knowledge production functions would rely on city- and industry-specific fixed effects to allow for differences in the level of innovation by firms located in different cities and operating in different industries. This approach however ignores the fact that, spatial dependence between cities and interindustry dependence arising from input-output relationships, may imply interaction, not simply heterogeneity across cities and industries.

We construct a Bayesian hierarchical model that allows for both city- and industry-level interaction (global spillovers) and subsumes other innovation scenarios such as: (1) heterogeneity that implies level differences (fixed effects) and (2) contextual effects that imply local spillovers as special cases.

The purpose of this paper is to study haemodynamic flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, magnetohydrodynamic (MHD) flow and aneurysm conditions. The findings of this study offer significant insights into the intricate interplay encompassing electro-osmosis, MHD flow, microorganisms, Joule heating and the ternary hybrid nanofluid.

The governing equations are first non-dimensionalised, and subsequently, a coordinate transformation is used to regularise the irregular boundaries. The discretisation of the governing equations is accomplished by using the Crank–Nicolson scheme. Furthermore, the tri-diagonal matrix algorithm is applied to solve the resulting matrix arising from the discretisation.

The investigation reveals that the velocity profile experiences enhancement with an increase in the Debye–Hückel parameter, whereas the magnetic field parameter exhibits the opposite effect, reducing the velocity profile. A comparative study demonstrates the velocity distribution in Au-CuO hybrid nanofluid and Au-CuO-GO ternary hybrid nanofluid. The results indicate a notable enhancement in velocity for the ternary hybrid nanofluid compared to the hybrid nanofluids. Moreover, an increase in the Brinkmann number results in an augmentation in entropy generation.

This study investigates the flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, MHD flow and aneurysm conditions. The governing equations are non-dimensionalised, and a coordinate transformation is applied to regularise the irregular boundaries. The Crank–Nicolson scheme is used to model blood flow in the presence of a ternary hybrid nanofluid (Au-CuO-GO/blood) within the arterial domain. The findings shed light on the complex interactions involving stenosis, MHD flow, aneurysms, Joule heating and the ternary hybrid nanofluid. The results indicate a decrease in the wall shear stress (WSS) profile with increasing stenosis size. The MHD effects are observed to influence the velocity distribution, as the velocity profile exhibits a declining nature with an increase in the Hartmann number. In addition, entropy generation increases with an enhancement in the Brinkmann number. This research contributes to understanding fluid dynamics and heat transfer mechanisms in bifurcated arteries, providing valuable insights for diagnosing and treating cardiovascular diseases.

We examine personnel policies and careers in public agencies, particularly how wages and promotion standards can partially offset a fundamental contracting problem: the inability of public-sector workers to contract on performance, and the inability of political masters to contract on forbearance from meddling. Despite the dual contracting problem, properly constructed personnel policies can encourage intrinsically motivated public-sector employees to invest in expertise, seek promotion, remain in the public sector, and work hard. To do so requires internal personnel policies that sort “slackers” from “zealots.” Personnel policies that accomplish this task are quite different in agencies where acquired expertise has little value in the private sector, and agencies where acquired expertise commands a premium in the private sector. Even with well-designed personnel policies, an inescapable trade-off between political control and expertise acquisition remains.

Importance sampling is a popular Monte Carlo method used in a variety of areas in econometrics. When the variance of the importance sampling estimator is infinite, the central limit theorem does not apply and estimates tend to be erratic even when the simulation size is large. The authors consider asymptotic trimming in such a setting. Specifically, the authors propose a bias-corrected tail-trimmed estimator such that it is consistent and has finite variance. The authors show that the proposed estimator is asymptotically normal, and has good finite-sample properties in a Monte Carlo study.

This chapter proposes a multiobjective model to design a Closed Loop Supply Chain (CLSC) network. The first objective is to minimize the total cost of the network, while the second objective is to minimize the carbon emission resulting from production, transportation, and disposal processes using carbon cap and carbon tax regularity policies. In the third objective, we maximize the service level of retailers by using maximum covering location as a measure of service level. To model the proposed problem, a physical programming approach is developed. This work contributes to the literature in designing an optimum CLSC network considering the service level objective and product substitution.

This chapter estimates heterogeneous productivity growth and spatial spillovers through industrial linkages in the United States and China from 1981 to 2010. The authors employ a spatial Durbin stochastic frontier model and estimates with a spatial weight matrix based on inter-country input–output linkages to describe the spatial interdependencies in technology. The authors estimate productivity growth and spillovers at the industry level using the World KLEMS database. The spillovers of factor inputs and productivity growth are decomposed into domestic and international effects. Most of the spillover effects are found to be significant and the spillovers of productivity growth offered and received provide detailed information reflecting interdependence of the industries in the global value chain (GVC). The authors use this model to evaluate the impact of a US–Sino decoupling of trade links based on simulations of four scenarios of the reductions in bilateral intermediate trade. Their estimation results and their simulations are as mentioned based on date that ends in 2010, as this is the only KLEMS data available for these countries at this level of industrial disaggregation. As the GVC linkages between the United States and China have expanded since the end of their sample period their results can be viewed as informative in their own right for this period as well as possible lower bounds on the extent of the spillovers generated by an expanding GVC.