3D (3 dimensional) Young diagram is a generalization of 2D Young diagram. In this paper, from the orthogonality of 3D Young diagrams and the properties in affine Yangian and its MacMahon ...representation, we obtain the Schur functions corresponding to 3D Young diagrams, which are called 3-Schur functions. 3-Schur functions are a generalization of Schur functions in the sense that when h1=1,h2=−1,h3=0, the 3-Schur functions of 3D Young diagrams become Schur functions of 2D Young diagrams, which is a special case of h1=h,h2=−1h,h3=1h−h. When h1=h,h2=−1h,h3=1h−h, the 3-Schur functions turn into the Jack symmetric polynomials of 2D Young diagrams by multiplying a coefficient. We will see that 3-Schur functions are symmetric about three coordinate axes.
3D fermions and affine Yangian Wang, Na
Nuclear physics. B,
August 2021, 2021-08-00, 2021-08-01, Letnik:
969
Journal Article
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2D (dimensional) Boson-Fermion correspondence is a well-known object. In this paper, we define 3D Fermions Γm→ and Γm→⁎ for any vertex m→ and the representation space F, we find that F is isomorphic ...to the vector space of 3D Young diagrams. Operators Γm→ and Γm→⁎ are defined with amplitudes, which are described by complex numbers e1,e2,e3 satisfying e1+e2+e3=0, then we find that Γm→ and Γm→⁎ have relations with the generators in affine Yangian, and states in F are corresponding to 3-Schur functions. We also discuss the slice of state in F, which corresponds to the slice of 3D Young diagram. Finally, we show that in special case, 3D Fermions and the representation space become ordinary 2D Fermions and charged zero Fermionic Fock space respectively.
Atomically ordered intermetallic nanoparticles are promising for catalytic applications but are difficult to produce because the high-temperature annealing required for atom ordering inevitably ...accelerates metal sintering that leads to larger crystallites. We prepared platinum intermetallics with an average particle size of <5 nanometers on porous sulfur-doped carbon supports, on which the strong interaction between platinum and sulfur suppresses metal sintering up to 1000°C. We synthesized intermetallic libraries of small nanoparticles consisting of 46 combinations of platinum with 16 other metal elements and used them to study the dependence of electrocatalytic oxygen-reduction reaction activity on alloy composition and platinum skin strain. The intermetallic libraries are highly mass efficient in proton-exchange-membrane fuel cells and could achieve high activities of 1.3 to 1.8 amperes per milligram of platinum at 0.9 volts.
The academic setting is a collection of diverse emotive needs that require skillful educators who can regulate and deal with them. Emotion regulation by language educators emphasizes the techniques ...that language educators use to regulate their emotions. In addition, English as a Foreign Language (EFL) teachers have a growing interest in examining the utilization of mindfulness-based methods to study and instruct a foreign language. Indeed, it is regarded as a strategy that has been connected to constructive encouragement when utilized as a managing technique for anxiety and worry. Concerning this, the goal of this mini review is to examine the function of mindfulness in regulating educators’ focus, emotion, manner, and contemplation. Some theoretical suggestions for educational situations are presented.
As the important source of natural fibers in the textile industry, cotton fiber quality and yield are often restricted to drought conditions because most of cotton plants in the world grow in the ...regions with water shortage. WRKY transcription factors regulate multiple plant physiological processes, including drought stress response. However, little is known of how the WRKY genes respond to drought stress in cotton. Our previous study revealed GhWRKY33 is leaf-specific and induced by drought stress. In this study, our data showed GhWRKY33 protein localizes to the cell nucleus and is able to bind to "W-box" cis-acting elements of the target promoters. Under drought stress, GhWRKY33 overexpressing transgenic Arabidopsis was withered much more quickly than wild type due to faster water loss. Moreover, GhWRKY33 transgenic plants displayed more tolerance to abscisic acid (ABA), relative to wild type. Expression of some drought stress-related genes and ABA-responsive genes were changed in the GhWRKY33 transgenic Arabidopsis with drought or ABA treatment. Collectively, our findings indicate that GhWRKY33 may act as a negative regulator to mediate plant response to drought stress and to participate in the ABA signaling pathway.
Summary
LIM domain proteins are cysteine‐rich proteins, and are often considered as actin bundlers and transcription factors in plants. However, the roles of XLIM proteins in plants (especially in ...cotton) remain unexplored in detail so far. In this study, we identified a cotton XLIM protein (GhXLIM6) that is preferentially expressed in cotton fiber during whole elongation stage and early secondary cell wall (SCW) synthesis stage. The GhXLIM6‐silenced transgenic cotton produces shorter fibers with thinner cell walls, compared with wild‐type (WT). GhXLIM6 protein could directly bind F‐actin and promote actin polymerization both in vitro and in vivo. It also acts as a transcription factor to suppress GhKNL1 expression through binding the PAL‐box element of GhKNL1 promoter, and subsequently regulate the expression of CesA genes related to cellulose biosynthesis and deposition in SCWs of cotton fibers. The cellulose content in fibers of GhXLIM6RNAi cotton is lower than that in WT. Taken together, these data reveal the dual roles of GhXLIM6 in fiber development. On one hand, GhXLIM6 functions in fiber elongation through binding to F‐actin to maintain the dynamic F‐actin cytoskeleton. On the other hand, GhXLIM6 fine‐tunes fiber SCW formation, probably through directly suppressing transcription of GhKNL1 to promote cellulose biosynthesis.
Significance Statement
GhXLIM6 plays dual roles in fiber development: GhXLIM6 functions in fiber elongation through binding to F‐actin to maintain the dynamic F‐actin cytoskeleton, and it also fine‐tunes fiber secondary cell wall formation probably through directly suppressing transcription of GhKNL1 to promote cellulose biosynthesis.
• Basic helix–loop–helix (bHLH) proteins are involved in transcriptional networks controlling a number of biological processes in plants. However, little information is known on the roles of bHLH ...proteins in cotton fibre development so far.
• Here, we show that a cotton bHLH protein (GhFP1) positively regulates fibre elongation. GhFP1 transgenic cotton and Arabidopsis plants were generated to study how GhFP1 regulates fibre cell elongation.
• Fibre length of the transgenic cotton overexpressing GhFP1 was significantly longer than that of wild-type, whereas suppression of GhFP1 expression hindered fibre elongation. Furthermore, overexpression of GhFP1 in Arabidopsis promoted trichome development. Expression of the brassinosteroid (BR)-related genes was markedly upregulated in fibres of GhFP1 overexpression cotton, but downregulated in GhFP1-silenced fibres. BR content in the transgenic fibres was significantly altered, relative to that in wild-type. Moreover, GhFP1 protein could directly bind to the promoters of GhDWF4 and GhCPD to activate expression of these BR-related genes.
• Therefore, our data suggest that GhFP1 as a positive regulator participates in controlling fibre elongation by activating BR biosynthesis and signalling. Additionally, homodimerisation of GhFP1 may be essential for its function, and interaction between GhFP1 and other cotton bHLH proteins may interfere with its DNA-binding activity.
In this paper, we firstly find that the multiplications HM(u1)HM(u2)⋯HM(uN) are tau functions of the KP hierarchy for any positive integer numbers M,N, where HM(z) is the generating function of Young ...diagrams in an 1×M box. Then as applications, we find that the general states and the scalar products of general states in the phase model and the XX0 model are all tau functions of the KP hierarchy. We also discuss the wave functions in these models.
SUMMARY
Upland cotton, the mainly cultivated cotton species in the world, provides over 90% of natural raw materials (fibers) for the textile industry. The development of cotton fibers that are ...unicellular and highly elongated trichomes on seeds is a delicate and complex process. However, the regulatory mechanism of fiber development is still largely unclear in detail. In this study, we report that a homeodomain‐leucine zipper (HD‐ZIP) IV transcription factor, GhHOX4, plays an important role in fiber elongation. Overexpression of GhHOX4 in cotton resulted in longer fibers, while GhHOX4‐silenced transgenic cotton displayed a “shorter fiber” phenotype compared with wild type. GhHOX4 directly activates two target genes, GhEXLB1D and GhXTH2D, for promoting fiber elongation. On the other hand, phosphatidic acid (PA), which is associated with cell signaling and metabolism, interacts with GhHOX4 to hinder fiber elongation. The basic amino acids KR‐R‐R in START domain of GhHOX4 protein are essential for its binding to PA that could alter the nuclear localization of GhHOX4 protein, thereby suppressing the transcriptional regulation of GhHOX4 to downstream genes in the transition from fiber elongation to secondary cell wall (SCW) thickening during fiber development. Thus, our data revealed that GhHOX4 positively regulates fiber elongation, while PA may function in the phase transition from fiber elongation to SCW formation by negatively modulating GhHOX4 in cotton.
Significance Statement
GhHOX4 promotes fiber elongation by directly regulating expressions of GhEXLB1D and GhXTH2D genes in cotton, but phosphatidic acid interacts with GhHOX4 to alter the nuclear localization of GhHOX4, thereby suppressing transcriptional regulation of GhHOX4 to downstream genes in the transition from fiber elongation to secondary cell wall (SCW) thickening.
A fault line selection approach on the basis of modified artificial bee colony optimization deep neural network (ACB-DNN) is presented to address the difficulties in choosing a fault line in electric ...current grounding systems for small electric currents. Matlab/Simulink is utilized to acquire the zero-sequence electric current in the faulty circuit, the training sample dataset of the modified deep neural network (DNN) is used to output the line selection result after training. The training time is reduced to a certain extent by enhancing the bee colony method to optimize the network’s weights. The simulation results show that this algorithm decreases training time, enhances judgment accuracy, and is robust to system topology, all of which fulfill the demands of real application.
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