On Complex Numbers in Higher Dimensions

The geometric approach to generalized complex and three-dimensional hyper-complex numbers and more general algebraic structures being based upon a general vector space structure and a geometric multiplication rule which was only recently developed is continued here in dimension four and above. To this end, the notions of geometric vector product and geometric exponential function are extended to arbitrary finite dimensions and some usual algebraic rules known from usual complex numbers are replaced with new ones. An application for the construction of directional probability distributions is presented.

Geometry of String Theory Compactifications

String theory is a leading candidate for the unification of universal forces and matter, and one of its most striking predictions is the existence of small additional dimensions that have escaped detection so far. This book focuses on the geometry of these dimensions, beginning with the basics of the theory, the mathematical properties of spinors, and differential geometry. It further explores advanced techniques at the core of current research, such as G-structures and generalized complex geometry. Many significant classes of solutions to the theory's equations are studied in detail, from special holonomy and Sasaki–Einstein manifolds to their more recent generalizations involving fluxes for form fields. Various explicit examples are discussed, of interest to graduates and researchers.

A Study of the Spatial Effects of Financial Support and Economic Growth under Optimal Control of Nonlinear Generalized Complex Systems

This paper provides an in-depth analysis and study of the spatial effects of financial support and economic growth with the help of nonlinear generalized complex systems. Taking the industrial sector as the research object and combining the relevant contents of neoclassical investment theory, information economics, and institutional economics, this paper clearly defines and argues that the main feature of current financial policy is financial constraint rather than financial inhibition based on an in-depth understanding of the theoretical connotation and policy rationality of financial constraint and, as a premise, further analyzes the financial constraint policy causing excessive investment and capital mismatch in the corporate sector. It further analyzes the mechanism of the role of financial constraint policies in causing overinvestment and capital mismatch in the corporate sector and conducts empirical tests from three research perspectives of measuring investment efficiency, output efficiency of investment, allocation efficiency of industry capital, and investment behavior of microenterprises, and finally puts forward relevant policy recommendations in conjunction with the evaluation of the efficiency of financial constraint policies. This paper selects three dimensions of the financial system, namely, financial structure, financial efficiency, and financial scale, and studies the adaptability between these three dimensions and the development of the real economy, respectively, and then uses different empirical methods to analyze the dynamic adaptability effects between the development of the real economy and these three dimensions of the financial system and finally explores the way of adaptability between the financial system and the development of the real economy. This paper provides a medium and micro theoretical basis and new empirical evidence for understanding the importance of financial system reform on economic growth and also opens up a space for exploring the exit path of financial constraints and using interest rate marketization as a general grip to reasonably guide financial resources to achieve economic transformation and upgrading and sustainable and healthy development through supporting high-quality investment, using more interprovincial level data in the analysis, so it is more comprehensive and detailed than previous scholars’ studies. The examination is more comprehensive and detailed than previous scholars’ studies.

Dysautonomia Following Tetanus, Diphtheria, and Pertussis Vaccine (Tdap): The First Case of Extreme Cachexia Caused by Autoimmune/Inflammatory Syndrome Induced by Adjuvants (ASIA Syndrome) in a Human

Autoimmune/inflammatory Syndrome Induced by Adjuvants (ASIA; Shoenfeld’s syndrome) comprehends a group of autoimmune conditions that flourish in genetically predisposed individuals, following an external stimulus by the so-called adjuvants. Many adjuvants were described, such as vaccines, aluminum and other metals, silicone, tattoos, among others. Those conditions entail defined diseases, such as sarcoidosis and Sjogren’s syndrome, and generalized complex symptoms, for example, fatigue, sleep disturbance, orthostatic intolerance, and other dysautonomic manifestations. Those complaints were previously associated with autoantibodies against nervous system autonomic receptors, especially antibeta 1 adrenergic receptor antibodies, suggesting the autoimmune component of the condition. Here we report on a case of an 18-year-old woman who presented with extreme cachexia due to severe dysautonomia caused by the ASIA syndrome induced by the tetanus, diphtheria, and pertussis vaccine (Tdap).

Geometric Mechanics on Warped Product Semi-Slant Submanifold of Generalized Complex Space Forms

In this study, we develop a general inequality for warped product semi-slant submanifolds of type M n = N T n 1 × f N ϑ n 2 in a nearly Kaehler manifold and generalized complex space forms using the Gauss equation instead of the Codazzi equation. There are several applications that can be developed from this. It is also described how to classify warped product semi-slant submanifolds that satisfy the equality cases of inequalities (determined using boundary conditions). Several results for connected, compact warped product semi-slant submanifolds of nearly Kaehler manifolds are obtained, and they are derived in the context of the Hamiltonian, Dirichlet energy function, gradient Ricci curvature, and nonzero eigenvalue of the Laplacian of the warping functions.

Chen-Ricci Inequalities with a Quarter Symmetric Connection in Generalized Space Forms

In this article, we obtain improved Chen-Ricci inequalities for submanifolds of generalized space forms with quarter-symmetric metric connection, with the help of which we completely characterized the Lagrangian submanifold in generalized complex space form and a Legendrian submanifold in a generalized Sasakian space form. We also discuss some geometric applications of the obtained results.