Maximum Dimension Research Articles

Surfaces properties correlation with optical parameters of thickness dependent self-affine nanostructured SnS thin films: A study based on scaling law

Fractal concepts are employed to investigate the surface properties of tin sulfide (SnS) thin films, which are deposited on Fluorine-doped tin oxide (FTO)- coated glass substrates by the thermal evaporation (TE) technique. The surface topography of each deposited film is captured by AFM. The fractal dimensions of the AFM image were extracted through the Higuchi algorithm, and it is found that the thinner sample surface exhibits the maximum fractal dimension. The autocorrelation function and height-height correlation function are used to investigate the self-affinity behavior of surfaces. Dynamic surface roughening is characterized by different scaling exponents, such as the roughness exponent, the growth exponent, the dynamic scaling exponent, and the steepening exponent. It was observed that the values of average roughness, interface width, lateral correlation length, and mean square local slope are strongly influenced by film thickness. The self-affine fractal nature of thin film is estimated by the roughness exponent; however, island- or mound-type growth with quick surface roughening behavior is predicted by the growth exponent and the dynamic scaling exponent. Further, we have tried to correlate the optical properties such as transmission, reflection, and refractive index with the fractal dimension of SnS thin film. The increase in optical reflection with decreasing roughness indicates that absorber surfaces of the best crystalline films have the lowest reflectivity. The present results suggest that such surfaces, having a maximum fractal dimension and minimum optical reflectance, can be used as photon absorber layers for advanced solar cell devices.

Investigation on acoustic emission characteristics of fault stick-slip under different lateral pressures

To explore the effect of different stress environments on fault-slip rockbursts. Bidirectional shear friction experiments with different lateral pressures were conducted on precracked syenogranites buried at 800 m. The macroscopic statistical parameters (cumulative number of AE events, magnitude and b value) and local characteristic parameters (amplitude and dominant frequency) of acoustic emission during the stick-slip process under different lateral pressures were investigated. In addition, based on fractal theory, the nonlinear characteristics of AE spectrum were analyzed. On this basis, the microscopic mechanism of fault stick-slip was discussed. The results show that the lateral pressure influences the friction strength of the fault and stick-slip motion characteristics. With increasing lateral pressure, the proportion of transgranular shear fractures increases, which leads to an increase of cumulative number of AE events and magnitude. The periodic decrease in the b value is more significant at high lateral pressure. There is a good correlation between a high-magnitude AE event and a stress drop. The AE frequency with phased response characteristics can be used to effectively identify the evolution of fault stick-slip instability at the laboratory scale. A sharp increase in the amplitude of the dominant frequency can be regarded as one of the precursory features of fault stick-slip instability. The AE frequency spectra have multifractal characteristics, that differ among the different stages. The maximum multifractal dimension and spectral width can reflect the difference in energy released during fault stick-slip motion.

Porosity and phase composition effects on SHS-NiTi structure and mechanical properties

NiTi samples with 59–70% porosity were obtained by the self-propagating high-temperature synthesis (SHS) using Ti, Ni, and NiTi powders as inert. The maximum and average pore sizes increase, while the maximum and average dimensions of the bridges decrease with porosity, controlled by adjusting the amount of inert additives, based on the surface and cross-sectional microscopy studies. The phase composition of porous NiTi was determined by X-ray diffraction. The alloy contains an austenitic B2 TiNi phase, a martensitic B19′ TiNi phase, and a secondary Ti2Ni phase. SHS-NiTi samples with different porosity were tested by uniaxial compression, revealing mechanical properties’ dependence on porosity. It is shown that with an 11% increase in the NiTi alloy porosity, the yield and compressive strength are reduced by almost a factor of 2.

Pulmonary gangliocytic paraganglioma: An under-recognized mimic of carcinoid tumor

Gangliocytic paragangliomas are rare neoplasms occurring almost exclusively in the ampullary region of the gastrointestinal tract. Although these tumors are not typically considered in the differential diagnosis of primary pulmonary neoplasia, 5 cases of primary pulmonary gangliocytic paragangliomas have been previously reported. Herein we report our experience with 3 additional examples, all referred to our Anatomic Pathology Consultation service. The patients (a 32-year-old man, a 69-year-old woman and a 55-year-old man) each presented with an endobronchial (2 cases) or upper lobe lung mass, ranging from 1.5 to 2.5 cm in maximum dimension. Biopsy and endobronchial debulking specimens demonstrated the classic triphasic morphology of gangliocytic paraganglioma, with epithelial, spindled and ganglion-like cells. By immunohistochemistry, the tumors were positive for keratin, synaptophysin and chromogranin A in the epithelial component, S100 protein and glial fibrillary acidic protein (GFAP) in the Schwannian spindled cells, and synaptophysin in ganglion cells. TTF1 expression was seen in the epithelial components of 2 cases. The Ki-67 labelling index was low (<2%). Primary pulmonary gangliocytic paragangliomas should be distinguished from carcinoid tumors, given the different natural histories and risk stratification approaches for these morphologically similar tumors. Awareness that gangliocytic paraganglioma may occur in the lung and appropriate immunohistochemical studies are key to correct diagnosis.

The natural history of aneurysms incompletely occluded by placement of a flow diverter: a multiinstitutional study.

Treatment of intracranial aneurysms by flow diversion is safe and effective and is increasingly popular. However, the correct treatment paradigm for aneurysms incompletely treated by initial placement of a flow diverter has not been established, nor have the subsequent natural history and occlusion rates of such aneurysms. The authors sought to outline the natural history of such aneurysms, which to date have been considered partially treated. The authors retrospectively reviewed consecutive cases from 6 high-volume neurointerventional services, including all cases in which the first follow-up imaging after placement of a flow diverter showed incomplete occlusion of the aneurysm, and for which subsequent clinical and/or radiological follow-up was available. All included patients were treated with the Pipeline Flex embolization device or the Pipeline Flex embolization device with Shield Technology. Subsequent radiographic and clinical outcome data were collected and analyzed using the Kaplan-Meier survival function. A total of 263 patients with persistently patent aneurysms on first follow-up imaging after flow diversion were identified. Of these, 204 had clinical follow-up and 152 had additional imaging follow-up. Of this final cohort, 148 aneurysms were unruptured, and 4 were ruptured. The average aneurysm size by maximum dimension was 10.8 mm. The average recorded follow-up was 27.8 months in the cohort, with some patients followed for as long as 9 years from treatment. Over the course of 403 person-years of follow-up, no delayed aneurysm ruptures were recorded. Both with and without retreatment, aneurysms showed a trend toward progressive occlusion over time. Complications related to device placement were low. Aneurysms that have been incompletely treated by flow diversion have a benign natural history with progression toward occlusion over time, with or without retreatment.

Clinical and Operative Risk Factors Associated With Prolonged Length of Stay After Endoscopic Pituitary Adenoma Resection.

Pituitary adenomas (PAs) are the most common intrasellar tumor. Clinically relevant adenomas have a prevalence of 1 per 1000 in the general population. Transsphenoidal surgery (TSS) is the most common surgical treatment and is the first-line management for most PAs. Most patients fare well postoperatively, but a subset of patients experience a prolonged length of stay (PLOS). In this article, we aim to identify demographic and clinical factors associated with PLOS after TSS for PA. Patients with sellar pathologies surgically treated at a single tertiary center from March 1, 2009, to May 31, 2020, were retrospectively reviewed. All patients older than 18 years receiving nonemergent endoscopic TSS for pituitary adenoma were included. Clinical and demographic characteristics were analyzed using χ 2 -tests and student t -tests. For those factors with a P -value less than .01, multivariate logistic regression and negative binomial regression models were constructed to estimate the adjusted odds of PLOS across predictive factors. A total of 301 patients were included in the study. This cohort had an average age of 54.65 ± 15.06 years and an average body mass index of 29.47 ± 6.69. The median length of stay was 54.9 hours [25th-75th percentiles: 43.5-72.9]. Postoperative cerebrospinal fluid leak ( P < .01), postoperative diabetes insipidus (DI) ( P < .01), increased surgery duration ( P = .01), and elevated maximal tumor dimension ( P = .01) were predictive of PLOS in logistic regression. Increased surgery duration, previous pituitary radiation, intraoperative complications, and postoperative DI (all P < .01) were associated with increased rate of PLOS in negative binomial regression. Patients undergoing endoscopic TSS for PA resection demonstrate prolonged lengths of stay if they have higher tumor burden, have lengthier surgeries with intraoperative complications, or develop postoperative complications such as cerebrospinal fluid leak or DI. Careful monitoring of these factors will allow for better resource optimization, reducing costs to both the hospital and the patient.

Corrosion behavior of magnetron sputtering Fe31Cr20Al17Ti16Nb16 high entropy coating in liquid lead-bismuth eutectic with different oxygen concentration at 500 °C

The major concern of the structure integrity of lead cooled reactor is the corrosion behavior of fuel cladding and other core internal materials. Magnetron sputtering technology is adopted as an surface coating method to improve the corrosion resistance of nuclear fuel cladding exposed to liquid lead-bismuth eutectic (LBE). Fe31Cr20Al17Ti16Nb16 high entropy alloy (HEA) coatings were prepared on tubular ferritic/martensitic (F/M) steel which is the candidate fuel cladding material, and the corrosion behaviors of Fe31Cr20Al17Ti16Nb16 coatings in LBE are investigated in this work. F/M steel specimens with Fe31Cr20Al17Ti16Nb16 coatings were exposed to 500 °C stagnant liquid LBE with oxygen concentration of Co ≈ 1 × 10−4 wt% and Co ≈ 1 × 10−7 wt% for 1000 h respectively. The primary findings suggest that the oxygen content of LBE mainly affects the morphology of duplex oxide layers generated during corrosion process, which resulting from the different inward diffusion flux of oxygen. In oxygen-saturated (Co ≈ 1 × 10−4 wt%) LBE, the overall oxide layer exhibits bulging and incompact morphology and infiltration of Pb is probed at inner Cr2O3 oxide layer, larger-sized cavities (the observed maximum dimension reaches 233.5 nm) distribute close to the outer Fe3O4/FeCr2O4 layer; In oxygen-depleted (Co ≈ 1 × 10−7 wt%) LBE, duplex oxide layer presents relatively dense and uniform state, tiny cavities (observed maximum dimension is 38.3 nm) dispersing at the internal of oxide areas. Corrosion rates of the Fe31Cr20Al17Ti16Nb16 coatings under two oxygen situations are 2 orders of magnitude lower than uncoated F/M steel under same exposure condition, the oxide layers with better uniformity and density produced in Co ≈ 1 × 10−7 wt% LBE indicating the better application advantage of Fe31Cr20Al17Ti16Nb16 coatings in oxygen-depleted LBE.

On linear codes with random multiplier vectors and the maximum trace dimension property

Abstract Let C C be a linear code of length n n and dimension k k over the finite field F q m {{\mathbb{F}}}_{{q}^{m}} . The trace code Tr ( C ) {\rm{Tr}}\left(C) is a linear code of the same length n n over the subfield F q {{\mathbb{F}}}_{q} . The obvious upper bound for the dimension of the trace code over F q {{\mathbb{F}}}_{q} is m k mk . If equality holds, then we say that C C has maximum trace dimension. The problem of finding the true dimension of trace codes and their duals is relevant for the size of the public key of various code-based cryptographic protocols. Let C a {C}_{{\boldsymbol{a}}} denote the code obtained from C C and a multiplier vector a ∈ ( F q m ) n {\boldsymbol{a}}\in {\left({{\mathbb{F}}}_{{q}^{m}})}^{n} . In this study, we give a lower bound for the probability that a random multiplier vector produces a code C a {C}_{{\boldsymbol{a}}} of maximum trace dimension. We give an interpretation of the bound for the class of algebraic geometry codes in terms of the degree of the defining divisor. The bound explains the experimental fact that random alternant codes have minimal dimension. Our bound holds whenever n ≥ m ( k + h ) n\ge m\left(k+h) , where h ≥ 0 h\ge 0 is the Singleton defect of C C . For the extremal case n = m ( h + k ) n=m\left(h+k) , numerical experiments reveal a closed connection between the probability of having maximum trace dimension and the probability that a random matrix has full rank.

Abstract 113: Treatment of Tiny (≤ 3mm) Unruptured Middle Cerebral Artery Aneurysms Are Associated With High Risk of Procedural Complications: An Analysis of the Neurovascular Quality Initiative-Quality Outcomes Database

Introduction: Improved imaging modalities have led to an increased detection of intracranial aneurysms, many of which are small. While studies have shown that many ruptured intracranial aneurysms are small (≤7 mm), the natural history of tiny (≤3 mm) aneurysms, particularly in certain locations such as the middle cerebral artery (MCA) is thought to be relatively benign with a reported rupture rate of less than 0.5% per year. The objective of this study is to evaluate the safety and efficacy of treatment of tiny unruptured MCA aneurysms. Methods: The NVQI-QOD registry was queried for patients with tiny unruptured MCA aneurysms who underwent either microsurgical or endovascular repair. Tiny size was defined as an aneurysm with a maximum dimension of ≤3 mm. Demographics, aneurysm characteristics and treatment safety were queried. Safety data included intra-operative and post-operative complications. Outcomes included modified Rankin Score (mRS) at discharge and last follow up as well as aneurysm occlusion status at discharge. Results: Of 670 treated, unruptured MCA aneurysms, 43 were tiny (6.4%). The mean aneurysm width was 1.9 mm with a mean patient age of 56.3 years. The median pre-operative mRS was 0 (range 0-4). The majority of patients underwent microsurgery (27/43). The overall intra-operative complication rate was 7% (3/43) with an intra-operative rupture rate of 4.7% (2/43). The post-operative complication rate was 9.3% (4/43). New intracerebral hemorrhage occurred in 7% of patients (3/43) and unplanned return to OR occurred in 14.8% of patients who underwent microsurgery (4/27). There were no mortalities. 16.3% (7/43) of patients were discharged to inpatient rehabilitation or a skilled nursing facility. At discharge, 37 (88.1%) patients had complete aneurysm occlusion. In the subgroup of patients with recorded follow up data, only 40% (10/25) had a mRS of 0 at discharge and 40% (6/15) had an mRS of 0 at last follow up (median follow up: 165 days). Conclusions: Our analysis showed that treatment of tiny unruptured MCA aneurysms is associated with a high rate of complications. We suggest that many tiny, unruptured MCA aneurysms should be observed given that the morbidity associated with treatment is likely significantly higher than the risk of rupture.

Sequence entropy and mean sequence dimension for non-compact metric spaces

In this paper, we introduce an extension of topological sequence entropy and d-sequence entropy for a dynamical system on a non-compact metric space. Then we give some elementary properties of those sequence entropy. In particular, we establish a variational principle which states that for a class of sequences, the supremum of the measure-theoretic sequence entropies and the minimum of the d-sequence entropies always coincide, and they are not less than the topological sequence entropy. Finally, we introduce the concepts of mean sequence dimension and maximal pattern mean topological dimension and give some properties of them.

Morphometric characteristics of the abdominal surface of the diaphragm for various benefits

The dependence of the regional morphometric characteristics of the abdominal surface of the diaphragm on body shape was evaluated because the information available in the specialized literature on this issue differs significantly. The study was conducted on 30 corpses aged 50–70 years, who were embalmed using a special technology (preserving tissue elasticity, giving the diaphragm a physiological shape with deep exhalation by pumping air into the abdominal cavity). The objects were then frozen, abdominal organs were sequentially removed, and linear dimensions and areas of subdiaphragmatic, subhepatic, and splenic depressions, physiological openings (inferior vena cava, aorta, esophagus, and ligamentous apparatus of the upper floor of the peritoneal cavity), area nuda, diaphragm legs, and lumbar–rib triangles were examined. The results of the analysis of the morphometric parameters revealed significant statistically significant differences in the linear dimensions and areas of the right and left subdiaphragmatic, subhepatic, splenic depressions, and individual parts of the diaphragm in individuals with different body shapes. For these anatomical formations of the peritoneum, the highest values of morphometric parameters are characteristic of the brachymorphic form of the physique, except for the sizes of the lumbar–costal triangles, medial legs, and height of the diaphragm domes, which have the maximum dimensions with a dolichomorphic form. Attention was drawn to the significant differences in the area nuda between extreme forms of physique, which reached 59%. Statistically significant differences were found in the morphometric parameters of the abdominal surface of the diaphragm in mesomorphic and extreme forms of physique; however, they are characterized by smaller values, ranging from 8% to 42% for various parameters. Of particular importance is knowledge of the size of the studied parts of the diaphragm covered by the peritoneum during cytoreductive interventions. Anatomical studies performed on specially embalmed objects with preservation of tissue elasticity and the physiological shape of the diaphragm allow us to obtain its reliable morphometric characteristics.

Facet analysis in data envelopment analysis: some pitfalls of the CRS models

The nonparametric estimator of the Extended Facet reference technology for the Constant Returns to Scale case has attracted some attention, because the associated production frontier by construction does only include strongly efficient faces of maximal dimension, or strongly efficient faces that are part of such strongly efficient faces of maximal dimension. The strongly efficient faces of maximal dimension are denoted Full Dimensional Efficient Facets (FDEFs). The identification of such strongly efficient facets is facilitated by removing all inefficient and all strongly efficient but not extreme efficient DMUs from the estimation procedure of the technology set. Any face that i) is passing through the origin and with (s + m − 1) linear independent extreme efficient observed DMUs positioned on it and ii) with a normal vector with strict positive (strict negative) output (input) components, is a FDEF, where s (m) is the number of outputs (inputs). It is, however, not correct that every face that satisfies only i) is a FDEF. We denote a face (a subface) that satisfies only condition i) but not condition ii) for an AP-face (an AP-subface). It is proved that a radial projection of any output input combination in the estimated EXFA technology set is positioned on the strongly efficient frontier if and only if i) no AP-(sub)faces exist, ii) a regulaty condition RC1 is satisfied and only dual multiplier constraints corresponding to extreme efficient DMUs are included in the estimation. A test for the fulfillment of the condition that no AP-(sub)faces exist is provided.

Assouad-type dimensions of overlapping self-affine sets

We study the Assouad and quasi-Assoaud dimensions of dominated rectangular self-affine sets in the plane. In contrast to previous work on the dimension theory of self-affine sets, we assume that the sets satisfy certain separation conditions on the projection to the principal axis, but otherwise have arbitrary overlaps in the plane. We introduce and study regularity properties of a certain symbolic non-autonomous iterated function system corresponding to ``symbolic slices'' of the self-affine set. We then establish dimensional formulas for the self-affine sets in terms of the dimension of the projection along with the maximal dimension of slices orthogonal to the projection. Our results are new even in the case when the self-affine set satisfies the strong separation condition: in fact, as an application, we show that self-affine sets satisfying the strong separation condition can have distinct Assouad and quasi-Assouad dimensions, answering a question of the first named author.

Prognostic value of right ventricular trabecular complexity in patients with arrhythmogenic cardiomyopathy.

The present study aimed to investigate the incremental prognostic value of the right ventricular fractal dimension (FD), a novel marker of myocardial trabecular complexity by cardiac magnetic resonance (CMR) in patients with arrhythmogenic cardiomyopathy (ACM). Consecutive patients with ACM undergoing CMR were followed up for major cardiac events, including sudden cardiac death, aborted cardiac arrest, and appropriate implantable cardioverter defibrillator intervention. Prognosis prediction was compared by Cox regression analysis. We established a multivariable model supplemented with RV FD and evaluated its discrimination by Harrell's C-statistic. We compared the category-free, continuous net reclassification improvement (cNRI) and integrated discrimination index (IDI) before and after the addition of FD. A total of 105 patients were prospectively included from three centers and followed up for a median of 60 (48, 66) months; experienced 36 major cardiac events were recorded. Trabecular FD displayed a strong unadjusted association with major cardiac events (p < 0.05). In the multivariable Cox regression analysis, RV maximal apical FD maintained an independent association with major cardiac events (hazard ratio, 1.31 (1.11-1.55), p < 0.002). The Hosmer-Lemeshow goodness of fit test displayed good fit (X2 = 0.68, p = 0.99). Diagnostic performance was significantly improved after the addition of RV maximal apical FD to the multivariable baseline model, and the continuous net reclassification improvement increased 21% (p = 0.001), and the integrated discrimination index improved 16% (p = 0.045). In patients with ACM, CMR-assessed myocardial trabecular complexity was independently correlated with adverse cardiovascular events and provided incremental prognostic value. The application of FD values for assessing RV myocardial trabeculae may become an accessible and promising parameter in monitoring and early diagnosis of risk factors for adverse cardiovascular events in patients with ACM. • Ventricular trabecular morphology, a novel quantitative marker by CMR, has been explored for the first time to determine the severity of ACM. • Patients with higher maximal apical fractal dimension of RV displayed significantly higher cumulative incidence of major cardiac events. • RV maximal apical FD was independently associated with major cardiac events and provided incremental prognostic value in patients with ACM.

Segmentation of the fibrillar layer in advanced fuchs endothelial corneal dystrophy: Inter‐oberserver‐reliability and intra‐observer‐repeatability analysis of corneal densitometry images

Aims: Our previous studies state that a central subendothelial collagen‐rich fibrillar layer (FL) is present in about 80% of advanced Fuchs endothelial corneal dystrophy (FECD) corneas which correlates with decreased corneal endothelial cell density and focal oedema formation. In this study, we investigated the previously unknown inter‐observer reliability and intra‐observer reproducibility of FL segmentation on Scheimpflug corneal densitometry images in patients with advanced FECD.Methods: Preoperative Scheimpflug images of patients receiving DMEK or triple DMEK for advanced FECD were retrospectively analysed. FL‐negative cases were excluded. Images were manually segmented with the open‐source software MITK by two experienced graders. A MATLAB‐based code calculated the region of interest (ROI) area, maximum calliper length, maximum horizontal and vertical dimension, and Dice similarity coefficient for FL‐areas. The intraclass correlation coefficient (ICC) was calculated by IBM SPSS (two‐way mixed, average measures). The FL localization on corneal densitometry were visualized by spatial heatmaps by MATLAB.Results: Among 308 eyes, 248 were FL‐positive (80.5%) and 60 FL‐negative (19.5%). The average Dice similarity coefficient of FL areas segmented by two graders was calculated at 0.85. Calculations on the segmentations of Grader 1 vs. Grader 2 include: ROI 7.91mm2 ± 4.8 vs. 9.29 mm2 ± 5.0, Calliper length 4.07 mm ± 1.1 vs. 4.21 mm ± 1.0, maximum horizontal dimension 3.85 mm ± 1.1 vs. 3.95 mm ± 1.0, maximum vertical dimension 3.17 mm ± 1.0 vs. 3.3 mm ± 1.0. The ICC was calculated at 0.938 vs. 0.957 vs. 0.930 for ROI (0.955 vs. 0.960 vs. 0.944 calliper length, 0.958 vs. 0.959 vs. 0.946 maximum horizontal dimension, 0.952 vs. 0.941 vs. 0.945 maximum vertical dimension) and 0.85 vs. 0.86 vs. 0.89 for the Dice similarity coefficient (inter‐observer vs. intra‐observer Grader 1 vs. intra‐observer Grader 2). Spatial heatmap analysis demonstrated primarily inferotemporal localization of increased densitometry areas in FL‐positive eyes.Conclusions: FL segmentation on corneal densitometry images exhibit high inter‐observer reliability and intra‐observer reproducibility scores. We provide evidence for corneal densitometry images as a valid tool to detect FL in advanced FECD and confirm the inferotemporal corneal projection of FL.

Extended conformations of bifurcating electron transfer flavoprotein constitute up to half the population, possibly mediating conformational change.

Electron transfer bifurcation enables biological systems to drive unfavourable (endergonic) electron transfer by coupling it to favourable (exergonic) transfer of a second electron. In electron transfer flavoproteins (ETFs), a domain-scale conformational change is believed to sever the favourable pathway after a single electron has used it, thereby preventing the energy dissipation that would accompany exergonic transfer of the second electron. To understand the conformation change that participates in turnover, we have deployed small-angle neutron scattering (SANS) and computational techniques to characterize the bifurcating ETF from Acidaminococcus fermentans (AfeETF). SANS data reveal an overall radius of gyration (R g) of 30.1 ± 0.2 Å and a maximum dimension (D max) of 100 Å for oxidized AfeETF. These measurements are 4 Å and 30 Å larger, respectively, than those of any published bifurcating ETF structure. Thus, we find that none of the reported ETF structures can explain the observed scattering, nor can any individual conformation generated by either of our molecular dynamics protocols. To optimize ensembles best able to explain the SANS data, we adapted a genetic algorithm. Successful ensembles contained a compact conformation comparable to one of the crystallographically documented conformations, accompanied by a much more extended one, and these two conformations sufficed to account for the data. The extended conformations identified all have R gs at least 4 Å larger than those of any currently published ETF structures. However, they are strongly populated, constituting 20% of the population of reduced ETF and over 50% of the population of oxidized AfeETF. Thus, the published (compact) structures provide a seriously incomplete picture of the conformation of AfeETF in solution. Moreover, because the composition of the conformational ensemble changes upon reduction of AfeETF's flavins, interconversion of the conformations may contribute to turnover. We propose that the extended conformations can provide energetically accessible paths for rapid interconversion of the open and closed compact conformations that are believed essential at alternating points in turnover.

Some insights into rank conditions of vector subspaces

&lt;p&gt;We introduce the general notion of a rank on a vector space, which includes both tensor rank and conventional matrix rank, but incorporates other examples as well. Extending this concept, we investigate vector spaces consisting of vectors with a lower bound on their rank. Our main result shows that bases for such spaces of maximum dimension can be chosen to consist exclusively of vectors of minimal rank. This generalization extends the results of &lt;sup&gt;[&lt;xref ref-type="bibr" rid="b15"&gt;15&lt;/xref&gt;,&lt;xref ref-type="bibr" rid="b36"&gt;36&lt;/xref&gt;]&lt;/sup&gt;, with potential applications in different areas.&lt;/p&gt;

О дифференцированиях линейных алгебр специального типа

In this work, Lie algebras of differentiation of linear algebra, the op­eration of multiplication in which is defined using a linear form and two fixed elements of the main field are studied. In the first part of the work, a definition of differentiation of linear algebra is given, a system of linear homogeneous equations is obtained, which is satisfied by the components of arbitrary differentiation. An embedding of the Lie algebra of differenti­ations into the Lie algebra of square matrices of order n over the field P is constructed. This made it possible to give an upper bound for the dimen­sion of the Lie algebra of derivations. It has been proven that the dimen­sion of the algebra of differentiation of the algebras under study is equal to n2 – n, where n is the dimension of the algebra. Next we give a result on the maximum dimension of the Lie algebra of derivations of a linear alge­bra with identity. Based on the above facts, it is proven that the algebras under study cannot have a unit.

The New Parthian Inscription from New Nisa

The article publishes a fragment of a ceramic vessel with a Parthian inscription preserved on it, discovered in 2012 at the site of New Nisa (Turkmenistan), approximately 120 m northeast of Tower XIII, and currently kept in a private collection in Russia. A small sherd (maximum dimensions 73×45 mm) 5–8 mm thick is most likely a fragment of a jug covered with white engobe. It is possible that, judging by the color of the engobe and the shard in the fracture, as well as the use of a high-temperature oxidative firing regime, the jug was made not in Parthyene, but in Margiana. A one-line inscription written in black paint or ink, of which only nine characters have come down to us, is located on the outside of the vessel, apparently on its hangers. The surviving part of the inscription reads ](y/z) ZNH ʻL wt(?)[. Its translation reads: “[The vessel] is for Vat...” It is possible that the name of the owner of the jug read as Wtpn (*Vātapāna) – “having the protection of the wind(-god)”, known from an Aramaic inscription from Persepolis. Judging by the fact that there is no hint of cursive in the inscription – each letter is written separately, it can be dated in the same way as the entire body of documents from Old Nisa, i.e. e second half of the 2nd – end of the 1st centuries BC.

Mechanical Characterisation of Bond Formation during Overprinting of PEEK Laminates.

The latest generation of high-temperature 3D printers enables the production of complex structural components from aerospace-grade thermoplastics such as PEEK (polyether ether ketone). However, adding long or continuous fibres is currently limited, and thermal stresses introduced during the process restrict the maximum part dimensions. Combining 3D-printed components with continuous fibre-reinforced components into one hybrid structure has the potential to overcome such limitations. This work aims to determine whether in situ bonding between PEEK laminates and PEEK 3D printing during overprinting is feasible and which process parameters are significantly responsible for the bonding quality. To this end, the bonding is analysed experimentally in two steps. Firstly, the influence of the process parameters on the thermal history and the strength of the bond is investigated. In the second step, a detailed investigation of the most critical parameters is carried out. The investigation showed the feasibility of overprinting with bonding strengths of up to 15 MPa. It was shown that the bonding strength depends primarily on the temperature in the interface. Additionally, the critical parameters to control the process were identified. The process influences that were displayed form the basis for future hybrid component and process designs.