New construction of mutually unbiased bases for odd-dimensional state space

We study the construction of mutually unbiased bases in Hilbert space for composite dimensions d which are not prime powers.We explore the results for composite dimensions which are true for prime power dimensions.We then provide a method for selecting mutually unbiased vectors from the eigenvectors of generalized Pauli matrices to construct mutually unbiased bases.In particular,we present four mutually unbiased bases in C^(15).

Research on the Construction and Development of Aesthetic Education Bases in Higher Education Institutions

In order to implement the national aesthetic education policy,it is essential to organically integrate relevant aesthetic education resources,promote interdisciplinary education,and carry out extracurricular practical activities centered on aesthetic education.Strengthening the foundation of aesthetic education theory,addressing practical challenges in the teaching process,and closely linking research with teaching will create a feedback loop that benefits drama education.This article provides an in-depth analysis of the construction strategies,resource advantages and disadvantages,and development of aesthetic education bases,offering countermeasures and suggestions for their construction in universities.It aims to provide a solid research foundation for the growth and development of aesthetic education bases in higher education institutions.

Homogenization Construction of Three-Level Teaching Bases for General Practice Medicine Under the Internet+Model

With the continuous expansion of medical student enrollment,the number of clinical teaching bases is gradually increasing.However,there are significant differences in clinical teaching management models and teaching levels among different bases.Most clinical teaching bases have incomplete teaching management systems,inadequate teaching management institutions,insufficient teaching personnel,and inadequate implementation of teaching rules and regulations.This article combines the construction practice of three-level clinical teaching base of the General Medicine College and the First Affiliated Hospital of Xi’an Medical University.We establish a standardized management system for the three-level clinical teaching base;implement a teaching supervision system and strengthen the monitoring of teaching quality;adopt multiple evaluations to test the effectiveness of clinical teaching implementation;explore the path of homogenization construction of teaching bases in terms of unified teacher training,promoting the development of teacher teaching abilities with equal quality and excellence,and providing a reference for improving the quality of medical talent training.

The Skew-commutator Relations and Grobner-Shirshov Bases of Quantum Group of Type c3

In this paper,we give a Grobner-Shirshov basis of quantum group of type C3 by using the Ringel-Hall algebra approach.For this,first we compute all skew-commutator relations between the isoclasses of indecomposable reprersentations of Ringel-Hall algebras of type C3 by using an“inductive”method.Precisely,we do not use the traditional way of computing the skew-commutative relations,that is first compute all Hall polynomials then compute the corresponding skew-commutator relations;contrarily,we compute the“easier”skew-commutator relations which corresponding to those exact sequences with middile term indecomposable or the split exact sequences first,then“inductive”others from these“easier”ones and this in turn gives Hall polynomials as a byproduct.Then we prove that the set of these relations is closed under composition.So they constitutes a minimal Grobner-Shirshov basis of the positive part of quantum group of type C3.Dually,we get a Grobner-Shirshov basis of the negative part of quantum group of type C3.And finally we give a Grobner-Shirshov basis for the whole quantum group of type C3.

Grobner-Shirshov Bases for Replicated Algebras

We establish a universal approach to solutions of the word problem in the varieties of di- and tri-algebras. This approach, for example, allows us to apply Grobner-Shirshov bases method for Lie algebras to solve the ideal membership problem in free Leibniz algebras （Lie di-algebras）. As another application, we prove an analogue of the Poincare-Birkhoff-Witt Theorem for universal enveloping associative tri-algebra of a Lie tri-algebra （CTD!-algebra）.

Physiological and molecular bases of the boron deficiency response in tomatoes

Boron is an essential microelement for plant growth.Tomato is one of the most cultivated fruits and vegetables in the world,and boron deficiency severely inhibits its yield and quality.However,the mechanism of tomato in response to boron deficiency remains largely unclear.Here,we investigated the physiological and molecular bases of the boron deficiency response in hydroponically grown tomato seedlings.Boron deficiency repressed the expression of genes associated with nitrogen metabolism,while it induced the expression of genes related to the pentose phosphate pathway,thereby altering carbon flow to provide energy for plants to cope with stress.Boron deficiency increased the accumulation of copper,manganese and iron,thereby maintaining chlorophyll content and photosynthetic efficiency at the early stage of stress.In addition,boron deficiency downregulated the expression of genes involved in cell wall organization and reduced the contents of pectin and cellulose in roots,ultimately retarding root growth.Furthermore,boron deficiency markedly altered phytohormone levels and signaling pathways in roots.The contents of jasmonic acid,jasmonoy1-L-isoleucine,trans-zeatin riboside,abscisic acid,salicylic acid,and SA glucoside were decreased;in contrast,the contents of isopentenyladenine riboside and ethylene precursor 1-aminocyclopropane-1-carboxylic acid were increased in the roots of boron-deficient tomato plants.These results collectively indicate that tomato roots reprogram carbon/nitrogen metabolism,alter cell wall components and modulate phytohormone pathways to survive boron deficiency.This study provides a theoretical basis for further elucidating the adaptive mechanism of tomato in response to boron deficiency.

Synthesis, Characterization and Biological Activity Evaluation of Schiff Bases Derived from 1,8-Diaminonaphtalène

The compounds have been synthesized and characterized by routine MS, IR and NMR spectrometry methods. The compounds are all active on bacterial strains with the exception of Salmonella typhimirium, with a MIC value of 7.5 mg/mL. They show a percentage of anti-radical activity of 75.476 ± 5.070 for the compound DAN-S and of 68.142 ± 6.539 for the compound DAN-OV. The compounds are sensitive to the two champions used. DAN-S compound is then the most active.

Jacobson＇s Lemma via Grobner-Shirshov Bases

Let R be a ring with identity 1. Jacobson＇s lemma states that for any a, b ∈ R, if 1 - ab is invertible then so is 1 - ba. Jacobson＇s lemma has suitable analogues for several types of generalized inverses, e.g., Drazin inverse, generalized Drazin inverse, and inner inverse. In this note we give a constructive way via Grobner-Shirshov basis theory to obtain the inverse of 1 - ab in terms of （1 - ba）-1, assuming the latter exists.

Solving the k-Independent Sets Problem of Graphs by Gröbner Bases

The aim of this paper is to given an algebraic computational method for finding maximal independent sets as well as the independent number of an arbitrary finite graph of n vertices G by strengthening the problem of finding maximal independent sets of G to the problem of finding k-independent sets in G for. It is shown that the existence of k-independent sets in G is equivalent to the existence of solutions of a system of multivariate polynomial equations. It follows that the problem of finding k-independent sets can be realized by using Gröbner bases of polynomial ideals. Since the number of k-independent sets is finite, the triangular equations composed by Gröbner bases are easier to be solved. Consequently, the maximal independent sets and the independent number of G are obtained after solving at most n such equations. Finally, the numerical example is presented to illustrate the effectiveness of this algebraic computational method.

A comprehensive review of lunar lava tube base construction and field research on a potential Earth test site

The Moon,as the closest celestial body to the Earth,plays a pivotal role in the progression of deep space exploration,and the establishment of research outposts on its surface represents a crucial step in this mission.Lunar lava tubes are special underground caves formed by volcanic eruptions and are considered as ideal natural shelters and scientific laboratories for lunar base construction.This paper begins with an in-depth overview of the geological origins,exploration history,and distribution locations of lunar lava tubes.Subsequently,it delves into the presentation of four distinctive advantages and typical concepts for constructing bases within lava tubes,summarizing the ground-based attempts made thus far in lunar lava tube base construction.Field studies conducted on a lava tube in Hainan revealed rock compositions similar to those found during the Apollo missions and clear lava tube structures,making it a promising analog site.Lastly,the challenges and opportunities encountered in the field of geotechnical engineering regarding the establishment of lunar lava tube bases are discussed,encompassing cave exploration technologies,in-situ testing methods,geomechanical properties under lunar extreme environments,base design and structural stability assessment,excavation and reinforcement techniques,and simulated Earth-based lava tube base.

Novel Mannich Bases of Benzimidazole Derivatives: An Antibacterial Study of Environmental Bacterial Strains

A previous study was conducted on the synthesis and antibacterial evaluation of Mannich bases of 2-(thioalkyl)-1H-methylbenzimidazole derivatives. The results of this study showed that certain 2-(thioalkyl)-1H-methylbenzimidazole and 2-(thioalkyl)-methyl-1-(piperidin-1-ylmethyl)benzimidazole derivatives possess antibacterial activities against clinical strains, such as Escherichia coli, Klebsiella pneumonia (Gram-negative bacteria), Staphylococcus aureus and Pseudomonas aeruginosa (Gram-positive bacteria). Following these favorable results, we extended the antibacterial evaluation of this series of molecules to environmental strains. The aim of this study was to assess the impact of the methyl-piperidine group fixed at position-1 of this new series of benzimidazoles on the antibacterial activity of environmental strains. In addition, we first evaluated the antibacterial activity of four 2-(thioalkyl)methylbenzimidazole derivatives and then that of five 2-(thioalkyl)-methyl-1-(piperidin-1-ylmethyl) benzimidazole derivatives. This study allowed us to show that compounds 1d and 1e could inhibit bacterial growth in vitro of the Enterobacteria P1 strain with inhibition diameters of 17.3 ± 0.6 mm and 10 ± 0.0 mm, respectively. However, addition of methyl-piperidinyl in this series showed that five (5) of 2-(thioalkyl)-methyl-1-(piperidin-1-ylmethyl) benzimidazole derivatives had an inhibitory effect on the in vitro growth of bacterial strains used except on Enterobacteria P2 with inhibition diameters between 10.0 ± 0.8 mm and 27.9 ± 1.4 mm. The introduction of the methyl-piperidinyl group at the 1-position of 2-(thioalkyl)-1H-methylbenzimidazole derivatives greatly improved the antibacterial activity against environmental bacteria such as Escherichia coli A1, A2, A3, and A4 and two Enterobacteria P1.

Imaging characteristics and treatment strategies for carotid artery occlusion caused by skull base fracture:Three case reports

BACKGROUND Traumatic internal carotid artery(ICA)occlusion is a rare complication of skull base fractures,characterized by high mortality and disability rates,and poor prognosis.Therefore,timely discovery and correct management are crucial for saving the lives of such patients and improving their prognosis.This article retrospectively analyzed the imaging and clinical data of three patients,to explore the imaging characteristics and treatment strategies for carotid artery occlusion,combined with severe skull base fractures.CASE SUMMARY This case included three patients,all male,aged 21,63,and 16 years.They underwent plain film skull computed tomography(CT)examination at the onset of their illnesses,which revealed fractures at the bases of their skulls.Ultimately,these cases were definitively diagnosed through CT angiography(CTA)examinations.The first patient did not receive surgical treatment,only anticoagulation therapy,and recovered smoothly with no residual limb dysfunction(Case 1).The other two patients both developed intracranial hypertension and underwent decompressive craniectomy.One of these patients had high intracranial pressure and significant brain swelling postoperatively,leading the family to choose to take him home(Case 2).The other patient also underwent decompressive craniectomy and recovered well postoperatively with only mild limb motor dysfunction(Case 3).We retrieved literature from PubMed on skull base fractures causing ICA occlusion to determine the imaging characteristics and treatment strategies for this type of disease.CONCLUSION For patients with cranial trauma combined with skull base fractures,it is essential to complete a CTA examination as soon as possible,to screen for blunt cerebrovascular injury.

Discussion on Construction and Mechanism of Practice Bases for Professional Degree Postgraduates Based on the Integration of Production and Education in Local Universities

Under the background of emerging agricultural education,practice bases are an important place to train profession talented person that match social needs,so it is very important to build stable and long-term practice bases.At present,the main problems in the construction of practice bases for postgraduates in local colleges and universities are mainly focusing on construction and neglecting management,imperfect cooperation mechanism and lack of teaching management effectively.It is of great significance to build a long-term management mechanism to ensure the education quality of practice bases.Therefore,constructing the mode of"double integration and double promotion of production and education"with practice bases as the carrier and realizing the organic combination of industrial needs and postgraduate projects is an important idea for local colleges and universities to train professional degree postgraduates to"know agriculture,love agriculture,strengthen agriculture and promote agriculture",and it also provides a reference for the mechanism construction of postgraduate bases.

Base Pressure Control with Semi-Circular Ribs at Critical Mach Number

When better fuel-air mixing in the combustion chamber or a reduction in base drag are required in vehicles,rockets,and aeroplanes,the base pressure control is activated.Controlling the base pressure and drag is necessary in both scenarios.In this work,semi-circular ribs with varying diameters(2,4,and 6 mm)positioned at six distinct positions(0.5D,1D,1.5D,2D,3D,and 4D)inside a square duct with a side of 15 mm are proposed as an efficient way to apply the passive control technique.In-depth research is done on optimising rib size for various rib sites.According to this study,the base pressure rises as rib height increases.Furthermore,the optimal location for the semi-circular ribs with a diameter of 2 mm is at 0.5D.The 1D location appears to be optimal for the 4 mm size as well.For the 6 mm size,however,the 4D position fills this function.

A novel fracture-cavity reservoir outcrop geological knowledge base construction method considering parameter collection and processing,mutual transformation of data-knowledge,application and update

This study endeavors to formulate a comprehensive methodology for establishing a Geological Knowledge Base(GKB)tailored to fracture-cavity reservoir outcrops within the North Tarim Basin.The acquisition of quantitative geological parameters was accomplished through diverse means such as outcrop observations,thin section studies,unmanned aerial vehicle scanning,and high-resolution cameras.Subsequently,a three-dimensional digital outcrop model was generated,and the parameters were standardized.An assessment of traditional geological knowledge was conducted to delineate the knowledge framework,content,and system of the GKB.The basic parameter knowledge was extracted using multiscale fine characterization techniques,including core statistics,field observations,and microscopic thin section analysis.Key mechanism knowledge was identified by integrating trace elements from filling,isotope geochemical tests,and water-rock simulation experiments.Significant representational knowledge was then extracted by employing various methods such as multiple linear regression,neural network technology,and discriminant classification.Subsequently,an analogy study was performed on the karst fracture-cavity system(KFCS)in both outcrop and underground reservoir settings.The results underscored several key findings:(1)Utilization of a diverse range of techniques,including outcrop observations,core statistics,unmanned aerial vehicle scanning,high-resolution cameras,thin section analysis,and electron scanning imaging,enabled the acquisition and standardization of data.This facilitated effective management and integration of geological parameter data from multiple sources and scales.(2)The GKB for fracture-cavity reservoir outcrops,encompassing basic parameter knowledge,key mechanism knowledge,and significant representational knowledge,provides robust data support and systematic geological insights for the intricate and in-depth examination of the genetic mechanisms of fracture-cavity reservoirs.(3)The developmental characteristics of fracturecavities in karst outcrops offer effective,efficient,and accurate guidance for fracture-cavity research in underground karst reservoirs.The outlined construction method of the outcrop geological knowledge base is applicable to various fracture-cavity reservoirs in different layers and regions worldwide.

Influence of external nitrogen-containing donors on polymerization behavior of neodymium-based cis-1,4-polybutadiene rubber

Neodymium(Nd)-based catalyst in butadiene(Bd)polymerization has drawn interests due to its availability in affording higher cis-1,4-unit selectivity than transition metal(Ti,Co,Ni,etc.)-based catalysts[1-2].Such outstanding high cis-1,4-unit selecti-vity is hypothetically originated from the presence of 4 f orbitals,that can participate in monomer coordination and thereby govern subsequent enchainment manners.This unique characteristic also renders the active species highly susceptible to Lewis bases,and may impact the overall selectivity as well as polyme-rization behavior after coordination.Nevertheless,it is still a virgin area in such a field,and the influence of Lewis bases on Nd-based diene polymerizations is still a black box.Based on this consideration,how nitrogen-containing donors(D)impacts the overall behaviors of Nd-mediated Bd polymerizations is disclosed.

The Evaluation of the Dietary Habits Influence on the Microhardness of Gingiva-Coloured Composite and Acrylic Denture Base Materials

Purpose: The study investigated the impact of dietary habits, specifically soda, milk kefir, water kefir, almond milk, and distilled water (control) consumption, on the microhardness of gingiva-coloured composite and acrylic denture bases. Methods: Materials included gingiva-coloured composite (Fusion Universal G1), acrylic (Imicryl), and subdivided Procryla group. Subgroups comprised 15 and 30-minute heat polymerized (Pro15, Pro30), and 1 wt% (Pro1Z) and 3 wt% (Pro3Z) zirconium added groups. Immersed in beverages for 1, 7, and 14 days, pH and microhardness were assessed. SEM examined random samples. Statistical analysis used repeated measures ANOVA, and post hoc tests (p Results: The gingiva-coloured composites displayed noteworthy time-associated microhardness changes (p 0.05). Despite variable pH levels in beverages, no substantial group interaction effects were observed (p > 0.05). Initial microhardness rankings shifted after a 14-day immersion. Conclusions: Gingiva-coloured composite exhibited the highest microhardness pre- and post-immersion, followed by Procryla30 and Imicryl groups. .

Source localization based on field signatures:Laboratory ultrasonic validation

Location awareness in wireless networks is essential for emergency services,navigation,gaming,and many other applications.This article presents a method for source localization based on measuring the amplitude-phase distribution of the field at the base station.The existing scatterers in the target area create unique scattered field interference at each source location.The unique field interference at each source location results in a unique field signature at the base station which is used for source localization.In the proposed method,the target area is divided into a grid with a step of less than half the wavelength.Each grid node is characterized by its field signature at the base station.Field signatures corresponding to all nodes are normalized and stored in the base station as fingerprints for source localization.The normalization of the field signatures avoids the need for time synchronization between the base station and the source.When a source transmits signals,the generated field signature at the base station is normalized and then correlated with the stored fingerprints.The maximum correlation value is given by the node to which the source is the closest.Numerical simulations and results of experiments on ultrasonic waves in the air show that the ultrasonic source is correctly localized using broadband field signatures with one base station and without time synchronization.The proposed method is potentially applicable for indoor localization and navigation of mobile robots.

Prediction of Damping Capacity Demand in Seismic Base Isolators via Machine Learning

Base isolators used in buildings provide both a good acceleration reduction and structural vibration control structures.The base isolators may lose their damping capacity over time due to environmental or dynamic effects.This deterioration of them requires the determination of the maintenance and repair needs and is important for the long-termisolator life.In this study,an artificial intelligence prediction model has been developed to determine the damage and maintenance-repair requirements of isolators as a result of environmental effects and dynamic factors over time.With the developed model,the required damping capacity of the isolator structure was estimated and compared with the previously placed isolator capacity,and the decrease in the damping property was tried to be determined.For this purpose,a data set was created by collecting the behavior of structures with single degrees of freedom(SDOF),different stiffness,damping ratio and natural period isolated from the foundation under far fault earthquakes.The data is divided into 5 different damping classes varying between 10%and 50%.Machine learning model was trained in damping classes with the data on the structure’s response to random seismic vibrations.As a result of the isolator behavior under randomly selected earthquakes,the recorded motion and structural acceleration of the structure against any seismic vibration were examined,and the decrease in the damping capacity was estimated on a class basis.The performance loss of the isolators,which are separated according to their damping properties,has been tried to be determined,and the reductions in the amounts to be taken into account have been determined by class.In the developed prediction model,using various supervised machine learning classification algorithms,the classification algorithm providing the highest precision for the model has been decided.When the results are examined,it has been determined that the damping of the isolator structure with the machine learning method is predicted successfully at a level exceeding 96%,and it is an effective method in deciding whether there is a decrease in the damping capacity.

Flexible,thermal processable,self-healing,and fully bio-based starch plastics by constructing dynamic imine network

The serious environmental threat caused by petroleum-based plastics has spurred more researches in developing substitutes from renewable sources.Starch is desirable for fabricating bioplastic due to its abundance and renewable nature.However,limitations such as brittleness,hydrophilicity,and thermal properties restrict its widespread application.To overcome these issues,covalent adaptable network was constructed to fabricate a fully bio-based starch plastic with multiple advantages via Schiff base reactions.This strategy endowed starch plastic with excellent thermal processability,as evidenced by a low glass transition temperature(T_(g)=20.15℃).Through introducing Priamine with long carbon chains,the starch plastic demonstrated superior flexibility(elongation at break=45.2%)and waterproof capability(water contact angle=109.2°).Besides,it possessed a good thermal stability and self-adaptability,as well as solvent resistance and chemical degradability.This work provides a promising method to fabricate fully bio-based plastics as alternative to petroleum-based plastics.