Quadratic Relations Research Articles

On the periods of twisted moments of the Kloosterman connection

AbstractThis paper aims to study the Betti homology and de Rham cohomology of twisted symmetric powers of the Kloosterman connection of rank two on the torus. We compute the period pairing and, with respect to certain bases, interpret these associated period numbers in terms of the Bessel moments. Via the rational structures on Betti homology and de Rham cohomology, we prove the $$\mathbb {Q}$$ Q -linear and quadratic relations among these Bessel moments.

Elliptic deformation of the Gaiotto-Rapčák corner VOA and the associated partially symmetric polynoimals

We construct the elliptic Miura transformation and use it to obtain the expression of the currents of elliptic corner VOA. We subsequently prove a novel combinatorial formula that is essential for deriving the quadratic relations of the currents. In addition, we give a conjecture that relates the correlation function of the currents of elliptic corner VOA to a certain family of partially symmetric polynomials. The elliptic Macdonald polynomials, constructed recently by Awata-Kanno- Mironov-Morozov-Zenkevich, and Fukuda-Ohkubo-Shiraishi, can be obtained as a particular case of this family.

Comparative investigation of activation energy and biot number on quadratic convective flow of a radiating micropolar fluid

In this study, we evaluate the significance of activation energy for initiating a chemical reaction in a two-dimensional laminar flow of a micropolar fluid over a semi-infinite inclined plate. The internal heat transfer mechanism of fluid is modeled with considerations of radiation and convective thermal boundary conditions. The momentum equation uses quadratic density relations in the concentration and temperature differences in buoyancy. In addition, flow through a porous medium surrounded by an inclined plate is modeled by the Darcy-Forchheimer model. Using a spectral successive linearization approach achieves the numerical results for the dimensionless equations. Basic characteristics of flow are examined for a range of dimensionless physical parameters. Quadratic convection is observed to have a stronger impact on the physical components of the flow than linear convection. In addition, compared to the linear illustration, the quadratic convection scenario results in a 14 % − 19 % increase in surface drag and heat transmission rate and a 5 % − 9 % decrease in mass transfer rate. Further, a higher activation energy corresponds with a higher concentration of micropolar fluid. Furthermore, as the radiation and Biot number rise, the velocity and rate of heat transfer correspondingly increase. We believe that the obtained results apply to aerosol technologies and polymeric mixtures used under extreme temperatures and concentrations.

Response of selected nutrient elements in leaf tissues of sweet potato cv. 'Bophelo' to Nemafric-BL phytonematicide

Nemafric-BL phytonematicide is a potent plant-based nematicide which consistently suppress nematode population densities of root-knot (Meloidogyne species) nematodes on various crops, but with limited information on its effects on foliar nutrient elements in sweet potato. The objective of this study, therefore, was to investigate the effects of Nemafric-BL phytonematicide on accumulation of nutrient elements in leaf tissues of sweet potato cv. 'Bophelo' under greenhouse conditions in Limpopo Province, South Africa, during autumn (February-April) in 2021 and validated in 2022. The product was applied weekly at geometric concentrations, with mature leaves collected and prepared for analysis of nutrient elements at eight weeks. Seasonal interactions were not significant and therefore data were pooled (n = 70) and then subjected to the Curve-fitting Allelochemical Response Dose (CARD) algorithm computer model. Iron (R2 = 0.86), K (0.91) and Na (0.82) versus Nemafric-BL phytonematicide each exhibited negative quadratic relations, whereas Zn (0.83) versus the product exhibited positive quadratic relations. In all test elements, the CARD-generated biological indices illustrated that the accumulation of elements was highly sensitive to the concentration of Nemafric-BL phytonematicide. In conclusion, in sweet potato production, the application of Nemafric-BL phytonematicide can inhibit (Fe, K) and stimulate (Zn) the accumulation of certain elements in leaf tissues of sweet potato cv. ′Bophelo‵.

Gauge origami and quiver W-algebras

We explore the quantum algebraic formalism of the gauge origami system in ℂ4, where D2/D4/D6/D8-branes are present. We demonstrate that the contour integral formulas have free field interpretations, leading to the operator formalism of qq-characters associated with each D-brane. The qq-characters of D2 and D4-branes correspond to screening charges and generators of the affine quiver W-algebra, respectively. On the other hand, the qq-characters of D6 and D8-branes represent novel types of qq-characters, where monomial terms are characterized by plane partitions and solid partitions. The composition of these qq-characters yields the instanton partition functions of the gauge origami system, eventually establishing the BPS/CFT correspondence.Additionally, we demonstrate that the fusion of qq-characters of D-branes in lower dimensions results in higher-dimensional D-brane qq-characters. We also investigate quadratic relations among these qq-characters. Furthermore, we explore the relationship with the representations, q-characters, and the Bethe ansatz equations of the quantum toroidal gl1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathfrak{gl}}_1 $$\\end{document}. This connection provides insights into the Bethe/Gauge correspondence of the gauge origami system from both gauge-theoretic and quantum-algebraic perspectives.We finally present conjectures regarding generalizations to general toric Calabi-Yau four-folds. These generalizations imply the existence of an extensive class of qq-characters, which we call BPS qq-characters. These BPS qq-characters offer a new systematic approach to derive a broader range of BPS/CFT correspondence and Bethe/Gauge correspondence.

Using social network analysis to investigate mathematical connections in U.S. and Chinese textbook problems

Textbooks, as potentially implemented curricula, play an important role in supporting classroom teaching and learning. Mathematical connections, one of the essential and hot topics advocated in mathematics education, have been emphasized in national curriculum reforms in various countries. However, little is known about the connection networks represented in school textbooks; even less has been done to compare textbooks from different countries. In this study, we propose an innovative method for examining how connections are represented in two popular U.S. (the UCSMP series) and Chinese (the PEP-A series) high school textbook problems involving quadratic relations. By using social network analysis, we identified 1129 connections, characterized connection networks into dense, moderate, and sparse digraphs, identified influential, prominent, and dual concepts and representations, and evaluated the strength between typical and reverse connections. The results revealed that the Chinese series presented a denser network of balanced between-concept connections but limited within-concept connections. The U.S. series exhibited more within-concept connections but emphasized typical connections, thus validating the potential of this innovative method. From this study, we suggest that our novel method provides a theoretical contribution to textbook analysis and connection analysis, which has rich implications for practice, for example, examining the network of connections students construct as a way to assess and to promote their conceptual understanding, and our approach opens the possibility of adopting new and efficient analytical tools from social network analysis in mathematics education research.

Impact of varied rates of NPK fertilizer on the microbial diversity of Jatropha zeyheri tea leaves under greenhouse conditions

Fertilization of Nitrogen (N), phosphorus (P) and potassium (K) is an effective strategy for improving tea yield and quality. Even though, NPK fertilization enhances tea yield and quality, addressing soil deficiencies to boost growth, but also impacts soil microbes, influencing nutrient cycling and yield. Therefore, the objective of this study was to assess the effect of different NPK fertilizer application rates on microbial composition of J. zeyheri tea under greenhouse conditions. Six treatments constituting NPK fertilizer rates (2:3:2 ratio) @ 0, 2, 4, 8, 16 and 32 g were arranged in a randomized complete block design, with five replications. 130 days after initiating treatments, leaves were harvested and oven-dried for 72 h at a temperature of 60°C. After laboratory preparations, microorganisms on tea leaves were determined by the principle most probable number using the Tempo reader (BioMerieux, Rodolphe, Durham, United States) instrument. Treatments had a highly significant effect (P ≤ 0.01) on Bacillus cereus contributing 39% in total treatment variation (TTV), whereas increasing NPK fertilizer rates had significant effects (P ≤ 0.05) on Enterobacteriaceae contributing 58% in TTV. Increasing rates of NPK fertilizer did not influence total coliforms contained in J. zeyheri tea leaf tissues. Bacillus cereus and Enterobacteriaceae over increasing NPK fertilizer rates exhibited positive quadratic relations, with density dependent growth pattern. Fertilizer requirements for Bacillus cereus and Enterobacteriaceae under greenhouse conditions were optimized at 1.75 g fertilizer/plant. In conclusion, Bacillus cereus and Enterobacteriaceae were affected by increasing NPK fertilizer rates.

Tau-functions beyond the group elements

Matrix elements in different representations are connected by quadratic relations. If matrix elements are those of a group element, i.e. satisfying the property Δ(X)=X⊗X, then their generating functions obey bilinear Hirota equations and hence are named τ-functions. However, dealing with group elements is not always easy, especially for non-commutative algebras of functions, and this slows down the development of τ-function theory and the study of integrability properties of non-perturbative functional integrals. A simple way out is to use arbitrary elements of the universal enveloping algebra, and not just the group elements. Then the Hirota equations appear to interrelate a whole system of generating functions, which one may call generalized τ-functions. It was recently demonstrated that this idea can be applicable even to a somewhat sophisticated case of the quantum toroidal algebra. We consider a number of simpler examples, including ordinary and quantum groups, to explain how the method works and what kind of solutions one can obtain.

Remarkable undercooling capability and metastable thermophysical properties of liquid Nb84.1Si15.9 alloy revealed by electrostatic levitation in outer space.

The stable manipulation, high undercooling, and thermophysical property measurement of the liquid Nb84.1Si15.9 refractory alloy were successfully achieved by the electrostatic levitation technique on board the China Space Station. By controlling the superheating temperature, a maximum liquid undercooling up to 421K (0.18 TL) was obtained in the space environment, and two distinct solidification paths with different recalescence features were realized at metastable undercooled states. The liquid density and the ratio of specific heat to emissivity were measured in a wide temperature range from 1841 to 2346K, which displayed linear and quadratic relations vs temperature, respectively. The liquid emissivity was further deduced from the specific heat of the liquid alloy calculated by molecular dynamics simulation. In addition, both the density and structural characteristics of the undercooled liquid alloy were also analyzed by MD calculations.

The R-matrix presentation for the rational form of a quantized enveloping algebra

Let Uq(g) denote the rational form of the quantized enveloping algebra associated to a complex simple Lie algebra g. Let λ be a nonzero dominant integral weight of g, and let V be the corresponding type 1 finite-dimensional irreducible representation of Uq(g). Starting from this data, the R-matrix formalism for quantum groups outputs a Hopf algebra URλ(g) defined in terms of a pair of generating matrices satisfying well-known quadratic matrix relations. In this paper, we prove that this Hopf algebra admits a Chevalley–Serre type presentation which can be recovered from that of Uq(g) by adding a single invertible quantum Cartan element. We simultaneously establish that URλ(g) can be realized as a Hopf subalgebra of the tensor product of the space of Laurent polynomials in a single variable with the quantized enveloping algebra associated to the lattice generated by the weights of V. The proofs of these results are based on a detailed analysis of the homogeneous components of the matrix equations and generating matrices defining URλ(g), with respect to a natural grading by the root lattice of g compatible with the weight space decomposition of End(V).

On the schematicness of some Ore polynomials of higher order generated by homogenous quadratic relations

In this paper, we investigate the property of schematicness introduced by Van Oystaeyen and Willaert [F. Van Oystaeyen and L. Willaert, Grothendieck topology, coherent sheaves and Serre’s theorem for schematic algebras, J. Pure Appl. Algebra 104(1–3) (1995) 109–122] in the setting of skew Ore polynomials of higher order generated by homogenous quadratic relations defined by Golovashkin and Maksimov [A. V. Golovashkin and V. M. Maksimov, Skew Ore polynomials of higher orders generated by homogeneous quadratic relations, Russian Math. Surveys 53(2) (1998) 384–386]. We establish sufficient conditions to guarantee whether some of these algebras are schematic or not.

Two-dimensional high-resolution numerical investigation of eddy effect in artificial rough conduits with different shapes

Subsurface conduit flow is a critical element of investigating groundwater movement in karst regions, and it is still poorly understood due to complexity of subsurface conduit geometries and the nonlinearity of the conduit flux-hydraulic gradient relationship. A significant nature of the flow nonlinearity is the occurrence of different eddies in conduits. To reveal the nonlinear nature of conduit flow, this study investigates the influence of the eddy effect on the hydraulic gradient of different rough conduits based on extensive high-fidelity numerical simulations. Overall, the hydraulic gradients of all types of rough conduits show quadratic relations with an increase in the specific discharge. In addition, the triangular rough conduit has the largest hydraulic gradient, which gradually decreases as the shape coefficient (which is used to quantify rough elements) increases. We have identified the development and evolution of eddies in different types of rough conduits in detail. This study shows that a larger specific discharge leads to a larger eddy area, and the hydraulic gradient changes exponentially with the eddy area ratio within a limited range. Finally, the relationships among specific discharges, eddy area ratio, and hydraulic gradients are constructed and summarized. The results of this investigation are helpful for developing realistic karst groundwater flow and transport models in which subsurface conduit plays a dominant role for conducting groundwater flux and mass transport.

NPK Fertilizer Requirements for Jatropha Zeyheri Indigenous Tea under Microplot Conditions

Effects of NPK fertilizer could have positive or negative effects in relation to growth of crops under certain environments, with minimum findings on how crops react to fertilizers under microplot conditions. Therefore, the objective of this study was to assess the effects of increasing NPK fertilizer rate on Jatropha zeyheri tea growth under microplot conditions. At two-leaf phase, J. zeyheri seedlings were transplanted into 25 cm diameter plastic pots. Each pot was filled with heated pasteurized sandy soil and Hygromix at 3:1 (v/v) ratio and placed in a spacing of 0.30 m × 0.30 m inter-and intra-row spacing. Six treatments constituting NPK fertilizer rates (0, 2, 4, 8, 16 and 32 g) were arranged in a randomized complete block design, with five replications. Treatments were initiated a week after transplanting, and 130 days after that, treatments had highly significant effects on leaf width, contributing 66% in TTV, whereas significant effects were reported on vine length, stem diameter, leaf length and dry root mass contributing 61, 67, 68 and 49% in TTV, respectively. NPK fertilizer rates did not affect chlorophyll content, NDVI, dry shoot mass, number of leaves and leaf area index. Jatropha zeyheri yield variables when exposed to increasing fertilizer rates displayed positive quadratic relations. Use of fertilizers had setbacks when applied inappropriately leading to inconsistent results. However, determining optimum fertilizer requirement for J. zeyheri was a strategical solution for inappropriate application. Jatropha zeyheri fertilizer requirements were optimized at 3.30 g fertilizer/plant, which shows that J. zeyheri requires a minimum amount of NPK fertilizer to stimulate growth.

Response of nutrient elements to Nemarioc-AL® phytonematicide in Swiss chard under greenhouse conditions

ABSTRACT Swiss chard (Beta vulgaris L. var. cicla) is susceptible to the root-knot nematodes (Meloidogyne spp.) since registered nematicides for this vegetable are not readily available. As a result, the noble product Nemarioc-AL® phytonematicide is currently used to manage plant parasitic nematodes on various crops. The product consistently suppressed nematode numbers. The efficacy of the product on nematode suppression was comparable to synthetic chemical nematicides. However, there is a lack of information on how the product will affect accumulation of nutrients in Swiss chard. Leaves of Swiss chard are an excellent source for Na and Mg; stems contain high K contents. The study was conducted to investigate how selected nutrient elements in Swiss chard would respond to concentrations of Nemarioc-AL® phytonematicide. Treatments ranging from 0% to 64% were applied weekly for 8 weeks. Potassium (K), Ca, Mg, Fe and Zn versus Nemarioc-AL® phytonematicide exhibited positive quadratic relations, with models explained by 96%, 79%, 64%, 78% and 77% associations, respectively. Increasing concentration of Nemarioc-AL® phytonematicide increased accumulation of selected nutrient elements in leaf tissues of Swiss chard.

Classification results for n-hereditary monomial algebras

We classify n-hereditary monomial algebras in three natural contexts: First, we give a classification of the n-hereditary truncated path algebras. We show that they are exactly the n-representation-finite Nakayama algebras classified by Vaso. Next, we classify partially the n-hereditary quadratic monomial algebras. In the case n=2, we prove that there are only two examples, provided that the preprojective algebra is a planar quiver with potential. The first one is a Nakayama algebra and the second one is obtained by mutating kA3⊗kkA3, where A3 is the Dynkin quiver of type A with bipartite orientation. In the case n≥3, we show that the only n-representation finite algebras are the n-representation-finite Nakayama algebras with quadratic relations.

ANCW: Affective norms for 4030 Chinese words.

Affective information contained in words is gaining increased attention among neurolinguists and psycholinguists around the world. This study established the Affective Norms for Chinese Words (ANCW) with valence, arousal, dominance, and concreteness ratings for 4030 words that were Chinese adaptations of the CET-4 (The National College English Test Band 4) official syllabus. Despite the existing Chinese affective norms such as the Chinese Affective Words System (CAWS), the ANCW provides much more and richer Chinese vocabulary. By using 7-point (ranging from 1 to 7) Likert scales in a paper-and-pencil procedure, we obtained ratings for all variables from 3717 Chinese undergraduates. The ANCW norms possessed good response reliability and were compatible with prior normative studies in Chinese. The pairwise correlation analysis revealed quadratic relations between valence and arousal, arousal and dominance, as well as valence and concreteness. Additionally, valence and dominance, as well as arousal and concreteness, presented a linear correlation, and concreteness and dominance were correlated. The ANCW provides reliable and standardized stimulus materials for further research involving emotional language processing.

Feynman diagrams in four-dimensional holomorphic theories and the Operatope

We study a class of universal Feynman integrals which appear in four-dimensional holomorphic theories. We recast the integrals as the Fourier transform of a certain polytope in the space of loop momenta (a.k.a. the “Operatope”). We derive a set of quadratic recursion relations which appear to fully determine the final answer. Our strategy can be applied to a very general class of twisted supersymmetric quantum field theories.

Effect of increased fertilization on the phytochemical constituents and antioxidant activity of Jatropha zeyheri tea under greenhouse conditions

Tea fertilization is one of the key factors influencing tea’s physiological, physical and chemical qualities. However, the influence of NPK fertilizer on phytochemical constituents and antioxidant activity of Jatropha zeyheri indigenous tea has not been documented. Therefore, this study aimed at assessing whether different fertilizer application rates would affect the phytochemical constituents and antioxidant activity of J. zeyheri tea leaves under greenhouse conditions. Six treatments constituting NPK fertilizer rates (0, 2, 4, 8, 16 and 32 g) were arranged in a randomized complete block design, with five replications. After 130 days, leaves were harvested and oven-dried for 72 h at a temperature of 60°C. The dried leaves were ground through a 1 mm sieve using a grinder before analysis. After laboratory preparations, phytochemicals and antioxidant activity were analyzed using the UV-visible spectrophotometer. Data were subjected to ANOVA using the Statistix 10.0 software. Treatments had a highly significant effect (P ≤ 0.01) on antioxidant activity and total flavonoid content contributing 46 and 73% in total treatment variation (TTV), respectively. In contrast, NPK fertilizer had a significant effect (P ≤ 0.05) on total phenols and tannins, contributing 71 and 59% in TTV, respectively. Jatropha zeyheri tea leaves antioxidants and phytoconstituents exhibited positive quadratic relations with increasing fertilizer levels. Fertilizer requirements for phytoconstituents and antioxidant activity were optimized at 3.97 g fertilizer/plant. In conclusion, antioxidant activity, total phenol, total tannin and flavonoid contents were affected by increasing NPK fertilizer rates.

Quadratic relations between periods of connections

We prove the existence of quadratic relations between periods of meromorphic flat bundles on complex manifolds with poles along a divisor with normal crossings under the assumption of "goodness". In dimension one, for which goodness is always satisfied, we provide methods to compute the various pairings involved. In an appendix, we give details on the classical results needed for the proofs. V3: Revised version, various proofs simplified in Section 3, exposition improved.

Nonlinear brain correlates of trait self-boundarylessness.

Alterations of the sense of self induced by meditation include an increased sense of boundarylessness. In this study, we investigated behavioural and functional magnetic resonance imaging correlates of trait self-boundarylessness during resting state and the performance of two experimental tasks. We found that boundarylessness correlated with greater self-endorsement of words related to fluidity and with longer response times in a math task. Boundarylessness also correlated negatively with brain activity in the posterior cingulate cortex/precuneus during mind-wandering compared to a task targeting a minimal sense of self. Interestingly, boundarylessness showed quadratic relations to several measures. Participants reporting low or high boundarylessness, as compared to those in between, showed higher functional connectivity within the default mode network during rest, less brain activity in the medial prefrontal cortex during self-referential word processing, and less self-endorsement of words related to constancy. We relate these results to our previous findings of a quadratic relation between boundarylessness and the sense of perspectival ownership of experience. Additionally, an instruction to direct attention to the centre of experience elicited brain activation similar to that of meditation onset, including increases in anterior precentral gyrus and anterior insula and decreases in default mode network areas, for both non-meditators and experienced meditators.