The Minimum-Norm Least Squares Solutions to Quaternion Tensor Systems

In this paper, we investigate the minimum-norm least squares solution to a quaternion tensor system A1*NX1=C1,A1*NX2+A2*NX3=C2,E1*NX1*MF1+E1*NX2*MF2+E2*NX3*MF2=D by using the Moore–Penrose inverses of block tensors. As an application, we discuss the quaternion tensor system A*NX=C,E*NX*MF=D for minimum-norm least squares reducible solutions. To illustrate the results, we present an algorithm and a numerical example

The Minimum-Norm Least Squares Solutions to Quaternion Tensor Systems

In this paper, we investigate the minimum-norm least squares solution to a quaternion tensor system A1*NX1=C1,A1*NX2+A2*NX3=C2,E1*NX1*MF1+E1*NX2*MF2+E2*NX3*MF2=D by using the Moore–Penrose inverses of block tensors. As an application, we discuss the quaternion tensor system A*NX=C,E*NX*MF=D for minimum-norm least squares reducible solutions. To illustrate the results, we present an algorithm and a numerical example

Analyzing Jeanne's Character and its Tragic Elements in Une vie from Hippolyte Adolphe Taine's 'Three Elements' Perspective

<p>This paper, following Hippolyte Adolphe Taine's "three elements" theory, delves into the factors contributing to Aunt Jeanne's personality and her tragic fate. Commencing with an examination of Aunt Jeanne's familial and life context, alongside the historical backdrop and the experiences of female characters like Joanna and the Baroness, this study applies Hippolyte Adolphe Taine's "three elements" - race, environment, and era - to facilitate a systematic analysis. This approach enables a deeper exploration of Aunt Jeanne's character and the tragic elements within her story. The study uncovered Aunt Jeanne as a tragic figure embodying trait such as timidity, sentimentality, low self-esteem, and heightened sensitivity.</p&gt

Combined Dispatching of Hydropower and Wind Power Based on the Hedging Theory

In order to improve the utilization rate of water resources in the flood season of the reservoir effectively and promote wind power consumption, this paper proposes an optimization model for the combined dispatching of wind power and hydropower based on the hedging theory. First, the conflicting relationship between the water storage benefits of hydropower stations, flood control risks, and the joint output of hydropower and wind power in joint dispatching is studied. The introduction of hedging theory divides the combined dispatching of wind power and hydropower into a two-stage dispatching problem including the decision-making stage and the remaining stage; Second, considering the uncertainty of water forecasting and wind power forecasting, a multi-objective optimal dispatching model of hydropower and wind power based on hedging theory is constructed. This model aims to minimize flood control risks, maximize water storage benefits, and minimize wind power and hydropower combined power output volatility. Finally, the non-dominated sorting genetic algorithm (NSGA2) is used to solve the specific examples. The results show that the model built in the article controls the flood control risk at each time period not to be higher than 1.63 × 10−3 (the flood control standard corresponding to the flood control risk in 50 years is 0.006). Additionally, the water level of the reservoir increased from the flood limit water level (583.00 m) to 583.70 m. It greatly increases the water storage capacity and effectively improves the utilization rate of water resources. At the same time, the optimized scheduling scheme reduced the peak-valley difference of joint output from 125.00 MW to 35.66 MW, and the peak-valley difference was greatly reduced. It effectively improves the volatility of wind power. The validity of the model is verified, and the obtained scheme can provide decision-making for the joint dispatch scheme of hydropower and wind power

Metabolomics Reveals Distinct Carbon and Nitrogen Metabolic Responses to Magnesium Deficiency in Leaves and Roots of Soybean [Glycine max (Linn.) Merr.]

Magnesium (Mg) deficiency, a widespread yet overlooked problem in agriculture, has been reported to retard plant growth and development, through affecting key metabolic pathways. However, the metabolic responses of plant to Mg deficiency is still not fully understood. Here we report a metabolomic study to evaluate the metabolic responses to Mg deficiency in soybean leaves and roots. Hydroponic grown soybean were exposed to Mg starvation for 4 and 8 days, respectively. Metabolic changes in the first mature trifoliolate leaves and roots were quantified by conducting GC-TOF-MS based metabolomic analysis. Principal component analysis (PCA) showed that Mg deficient plants became distinguishable from controls at 4 days after stress (DAS) at metabolic level, and were clearly discriminated at 8 DAS. Mg deficiency could cause large metabolite alterations on carbon and nitrogen metabolism. At 8 DAS, carbon allocation from shoot to root is decreased by Mg deficiency. Remarkably, most amino acids (such as phenylalanine, asparagine, leucine, isoleucine, glycine, glutamine, and serine) showed pronounced accumulation in the leaves, while most organic acids (including pyruvic acid, citric acid, 2-keto-glutaric acid, succinic acid, fumaric acid, and malic acid) were significantly decreased in the roots. Our study shows that the carbon and nitrogen metabolic responses are distinct in leaves and roots under Mg deficiency

Potential Regulatory Roles of MicroRNAs and Long Noncoding RNAs in Anticancer Therapies

MicroRNAs and long noncoding RNAs have long been investigated due to their roles as diagnostic and prognostic biomarkers of cancers and regulators of tumorigenesis, and the potential regulatory roles of these molecules in anticancer therapies are attracting increasing interest as more in-depth studies are performed. The major clinical therapies for cancer include chemotherapy, immunotherapy, and targeted molecular therapy. MicroRNAs and long noncoding RNAs function through various mechanisms in these approaches, and the mechanisms involve direct targeting of immune checkpoints, cooperation with exosomes in the tumor microenvironment, and alteration of drug resistance through regulation of different signaling pathways. Herein we review the regulatory functions and significance of microRNAs and long noncoding RNAs in three anticancer therapies, especially in targeted molecular therapy, and their mechanisms. Keywords: microRNAs, long noncoding RNAs, targeted therapy, chemoresistance, immune checkpoin