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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.

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.

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.

Key Clinical Message: We reported a 23‐year‐old male patient with panhypopituitarism who underwent two resections for craniopharyngioma and received postoperative hormone replacement therapy. The 99mTc‐MDP bone scan revealed focal high uptake of radioactive nuclide in multiple large joints. The SPECT/CT demonstrated the focal high uptake in their metaphysis. Thus, delayed epiphyseal closure was considered. [ABSTRACT FROM AUTHOR]

Key Clinical Message: A 57‐year‐old woman was diagnosed as lung adenocarcinoma. 99mTc‐MDP bone scan showed multiple radioactivity concentrated lesions on bilateral chest wall, which were confirmed as calcification foci after breast implant rupture by SPECT/CT. SPECT/CT could be used for differential diagnosis of breast implant rupture and malignant lesions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new generalized inverse, called the G-MPCEP inverse of a complex matrix. We investigate some characterizations, representations, and properties of this new inverse. Cramer's rule for the solution of a singular equation A x = B is also presented. Moreover, the determinantal representations for the G-MPCEP inverse are studied. Finally, the G-MPCEP inverse being used in solving appropriate systems of linear equations is established. [ABSTRACT FROM AUTHOR]

We report a case of accidental local 99mTc‐MDP uptake in left lung on bone scan without pulmonary parenchymal abnormality on SPECT/CT. The abnormal uptake disappeared on repeated bone scan and SPECT/CT after 3 days. It is speculated that the high radioactivity focus is a microthrombus in pulmonary artery. [ABSTRACT FROM AUTHOR]