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In this article, we study the m{\mathfrak{m}}-WG∘{}^{\circ } inverse which presents a generalization of the m{\mathfrak{m}}-WG inverse in the Minkowski space. We first show the existence and the uniqueness of the generalized inverse. Then, we discuss several properties and characterizations of the m{\mathfrak{m}}-WG∘{}^{\circ } inverse by using the core-EP decomposition. Applying the generalized inverse, we obtain the solutions of some matrix equations in Minkowski space.

Background Methods Results Conclusions Family caregivers of dementia patients face significant challenges, including managing their own emotional responses. Understanding factors influencing expressed emotion (EE) is crucial for effective support interventions. The aim of this study was to explore and describe changes in EE among family caregivers of dementia and its associated factors at different time points over 3 months.A 3‐month observational study was conducted in Japan. We collected demographically detailed data on family caregivers currently providing care, including care burden, relationship closeness, and depression. We assessed EE using the validated Family Attitude Scale (FAS). After adjustment for multiple confounding factors, multivariate linear regression analysis was performed to assess factors affecting EE at various time points. Linear regression analysis with generalised estimating equations was used to assess associations between 3‐month time‐varying EE and burden, intimacy, and depression.Fifty‐six family caregivers completed the study. Changes in FAS scores did not show statistical differences over 3 months. It is worth noting that the degree of relationship closeness and care burden are important influencing factors of EE in both cross‐sectional analysis and longitudinal analysis.Early identification of risk factors can aid in developing interventions aimed at preventing high levels of EE in the dementia family, thereby mitigating their detrimental effects. Tailored interventions are essential to enhance caregiver well‐being and cultivate positive caregiver–patient relationships. [ABSTRACT FROM AUTHOR]

While a majority of academic studies concerning acetone, butanol, and ethanol (ABE) production by Clostridium have focused on Clostridium acetobutylicum, other members of this genus have proven to be effective industrial workhorses despite the inability to perform genetic manipulations on many of these strains. To further improve the industrial performance of these strains in areas such as substrate usage, solvent production, and end product versatility, transformation methods and genetic tools are needed to overcome the genetic intractability displayed by these species. In this study, we present the development of a high-efficiency transformation method for the industrial butanol hyperproducer Clostridium saccharoperbutylacetonicum strain N1-4 (HMT) ATCC 27021. Following initial failures, we found that the key to creating a successful transformation method was the identification of three distinct colony morphologies (types S, R, and I), which displayed significant differences in transformability. Working with the readily transformable type I cells (transformation efficiency, 1.1 × 106 CFU/μg DNA), we performed targeted gene deletions in C. saccharoperbutylacetonicum N1-4 using a homologous recombination-mediated allelic exchange method. Using plasmid-based gene overexpression and targeted knockouts of key genes in the native acetone-butanol-ethanol (ABE) metabolic pathway, we successfully implemented rational metabolic engineering strategies, yielding in the best case an engineered strain (Clostridium saccharoperbutylacetonicum strain N1-4/pWIS13) displaying an 18% increase in butanol titers and 30% increase in total ABE titer (0.35 g ABE/g sucrose) in batch fermentations. Additionally, two engineered strains overexpressing aldehyde/alcohol dehydrogenases (encoded by adh11 and adh5) displayed 8.5- and 11.8-fold increases (respectively) in batch ethanol production. This paper presents the first steps toward advanced genetic engineering of the industrial butanol producer Clostridium saccharoperbutylacetonicum strain N1-4 (HMT). In addition to providing an efficient method for introducing foreign DNA into this species, we demonstrate successful rational engineering for increasing solvent production. Examples of future applications of this work include metabolic engineering for improving desirable industrial traits of this species and heterologous gene expression for expanding the end product profile to include high-value fuels and chemicals.

High-entropy carbides with controlled carbon content have the advantages of high thermal stability and good oxidation resistance, which give them potential for application as high-temperature microwave absorbing materials. In this study, (Co0.2Mo0.2V0.2Nb0.2Ta0.2)Cx high-entropy ceramic (HEC) powders are successfully prepared using a mechanical alloying method. Herein, reduction of the conductive graphite content leads to an increase in the concentration of carbon vacancies and a decrease in conductivity, which coordinates the polarization loss and conductivity loss capabilities. The dielectric loss capacity is enhanced by the combined effect of enhanced polarization loss and weakened conductivity loss. Simultaneously, the saturation magnetization intensity increases with the increase of carbon vacancy concentration, which leads to an enhanced magnetic loss capability. Ultimately, the sample (Co0.2Mo0.2V0.2Nb0.2Ta0.2)C0.8 with good impedance matching and attenuation ability achieves microwave absorption optimization at 293–573 K. The minimum reflection loss of (Co0.2Mo0.2V0.2Nb0.2Ta0.2)C0.8 reaches −57.77 dB (473 K) and the effective absorption bandwidth reaches 3.34 GHz (573 K), covering nearly 80% of the X-band with a thickness of only 2.2 mm. This work provides valuable insights into optimizing the high-temperature microwave absorption performance of high entropy carbides. [ABSTRACT FROM AUTHOR]

In this paper, we study the reverse order law for the Moore–Penrose inverse of the product of three bounded linear operators in Hilbert spaces. We first present some equivalent conditions for the existence of the reverse order law ABC†=C†B†A†. Moreover, several equivalent statements of ℛAA∗ABC=ℛABC and ℛC∗CABC∗=ℛABC∗ are also deducted by the theory of operators.

Recently, Ferreyra and Malik (Core and strongly core orthogonal matrices. Linear Multilinear Algebra. 2021;1–16. doi:) have proved that if A is strongly core orthogonal to B, then rk (A + B) = rk (A) + rk (B) and (A + B) ◯ # = A ◯ # + B ◯ # . But whether the reverse holds is an open question. In this paper, we solve the problem completely and get some new characterizations of strong core orthogonality. [ABSTRACT FROM AUTHOR]