Статті в журналах: "Rational Homogeneous variety"

1

Zhu, Yi. "HOMOGENEOUS SPACE FIBRATIONS OVER SURFACES." Journal of the Institute of Mathematics of Jussieu 18, no. 2 (April 3, 2017): 293–327. http://dx.doi.org/10.1017/s1474748017000081.

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By studying the theory of rational curves, we introduce a notion of rational simple connectedness for projective homogeneous spaces. As an application, we prove that over a function field of an algebraic surface over an algebraically closed field, a variety whose geometric generic fiber is a projective homogeneous space admits a rational point if and only if the elementary obstruction vanishes.

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2

Morishita, Masanori, and Takao Watanabe. "A note on the mean value theorem for special homogeneous spaces." Nagoya Mathematical Journal 143 (September 1996): 111–17. http://dx.doi.org/10.1017/s0027763000005948.

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Let G be a connected linear algebraic group and X an algebraic variety, both defined over Q, the field of rational numbers. Suppose that G acts on X transitively and the action is defined over Q. Suppose that the set of rational points X(Q) is non-empty. Choosing x ∈ X(Q) allows us to identify G/Gx and X as varieties over Q, there Gx is the stabilizer of x.

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3

Almeida, L. C. O., and S. C. Coutinho. "On Homogenous Minimal Involutive Varieties." LMS Journal of Computation and Mathematics 8 (2005): 301–15. http://dx.doi.org/10.1112/s1461157000001005.

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AbstractЅ(2n,k) be the variety of homogeneous polynomials of degree k in 2n variables. The authors of this paper give a computer-assisted proof that there is an analytic open set Ω of Ѕ(4,3) such that the surface F = 0 is a minimal homogeneous involutive variety of ℂ4 for all F ∈ Ω. As part of the proof, they give an explicit example of a polynomial with rational coefficients that belongs to Ω.

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4

Lee, Kyoung-Seog, and Kyeong-Dong Park. "Equivariant Ulrich bundles on exceptional homogeneous varieties." Advances in Geometry 21, no. 2 (April 1, 2021): 187–205. http://dx.doi.org/10.1515/advgeom-2020-0018.

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Abstract We prove that the only rational homogeneous varieties with Picard number 1 of the exceptional algebraic groups admitting irreducible equivariant Ulrich vector bundles are the Cayley plane E 6/P 1 and the E 7-adjoint variety E 7/P 1. From this result,we see that a general hyperplane section F 4/P 4 of the Cayley plane also has an equivariant but non-irreducible Ulrich bundle.

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5

Carrillo-Pacheco, Jesús, and Fausto Jarquín-Zárate. "A Family Of Low Density Matrices In Lagrangian–Grassmannian." Special Matrices 6, no. 1 (May 1, 2018): 237–48. http://dx.doi.org/10.1515/spma-2018-0019.

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Abstract The aim of this paper is twofold. First, we show a connection between the Lagrangian- Grassmannian variety geometry defined over a finite field with q elements and the q-ary Low-Density Parity- Check codes. Second, considering the Lagrangian-Grassmannian variety as a linear section of the Grassmannian variety, we prove that there is a unique linear homogeneous polynomials family, up to linear combination, such that annuls the set of its rational points.

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6

MOSSA, ROBERTO. "BALANCED METRICS ON HOMOGENEOUS VECTOR BUNDLES." International Journal of Geometric Methods in Modern Physics 08, no. 07 (November 2011): 1433–38. http://dx.doi.org/10.1142/s0219887811005841.

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Let E → M be a holomorphic vector bundle over a compact Kähler manifold (M, ω) and let E = E1 ⊕ ⋯ ⊕ Em → M be its decomposition into irreducible factors. Suppose that each Ej admits a ω-balanced metric in Donaldson–Wang terminology. In this paper we prove that E admits a unique ω-balanced metric if and only if [Formula: see text] for all j, k = 1,…, m, where rj denotes the rank of Ej and Nj = dim H0(M, Ej). We apply our result to the case of homogeneous vector bundles over a rational homogeneous variety (M, ω) and we show the existence and rigidity of balanced Kähler embedding from (M, ω) into Grassmannians.

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7

Huneke, Craig, and Matthew Miller. "A Note on the Multiplicity of Cohen-Macaulay Algebras with Pure Resolutions." Canadian Journal of Mathematics 37, no. 6 (December 1, 1985): 1149–62. http://dx.doi.org/10.4153/cjm-1985-062-4.

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Let R = k[X1, …, Xn] with k a field, and let I ⊂ R be a homogeneous ideal. The algebra R/I is said to have a pure resolution if its homogeneous minimal resolution has the formSome of the known examples of pure resolutions include the coordinate rings of: the tangent cone of a minimally elliptic singularity or a rational surface singularity [15], a variety defined by generic maximal Pfaffians [2], a variety defined by maximal minors of a generic matrix [3], a variety defined by the submaximal minors of a generic square matrix [6], and certain of the Segre-Veronese varieties [1].If I is in addition Cohen-Macaulay, then Herzog and Kühl have shown that the betti numbers bi are completely determined by the twists di.

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8

Müller, J. Steffen. "Explicit Kummer varieties of hyperelliptic Jacobian threefolds." LMS Journal of Computation and Mathematics 17, no. 1 (2014): 496–508. http://dx.doi.org/10.1112/s1461157014000126.

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AbstractWe explicitly construct the Kummer variety associated to the Jacobian of a hyperelliptic curve of genus 3 that is defined over a field of characteristic not equal to 2 and has a rational Weierstrass point defined over the same field. We also construct homogeneous quartic polynomials on the Kummer variety and show that they represent the duplication map using results of Stoll.Supplementary materials are available with this article.

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9

Alekseevsky, Dmitri V., Jan Gutt, Gianni Manno, and Giovanni Moreno. "Lowest degree invariant second-order PDEs over rational homogeneous contact manifolds." Communications in Contemporary Mathematics 21, no. 01 (January 28, 2019): 1750089. http://dx.doi.org/10.1142/s0219199717500894.

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For each simple Lie algebra [Formula: see text] (excluding, for trivial reasons, type [Formula: see text]), we find the lowest possible degree of an invariant second-order PDE over the adjoint variety in [Formula: see text], a homogeneous contact manifold. Here a PDE [Formula: see text] has degree [Formula: see text] if [Formula: see text] is a polynomial of degree [Formula: see text] in the minors of [Formula: see text], with coefficient functions of the contact coordinate [Formula: see text], [Formula: see text], [Formula: see text] (e.g., Monge–Ampère equations have degree 1). For [Formula: see text] of type [Formula: see text] or [Formula: see text], we show that this gives all invariant second-order PDEs. For [Formula: see text] of types [Formula: see text] and [Formula: see text], we provide an explicit formula for the lowest-degree invariant second-order PDEs. For [Formula: see text] of types [Formula: see text] and [Formula: see text], we prove uniqueness of the lowest-degree invariant second-order PDE; we also conjecture that uniqueness holds in type [Formula: see text].

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10

Chipalkatti, Jaydeep. "Apolar Schemes of Algebraic Forms." Canadian Journal of Mathematics 58, no. 3 (June 1, 2006): 476–91. http://dx.doi.org/10.4153/cjm-2006-020-3.

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AbstractThis is a note on the classical Waring's problem for algebraic forms. Fix integers (n, d, r, s), and let ∧ be a general r-dimensional subspace of degree d homogeneous polynomials in n+1 variables. Let denote the variety of s-sided polar polyhedra of ∧. We carry out a case-by-case study of the structure of for several specific values of (n, d, r, s). In the first batch of examples, is shown to be a rational variety. In the second batch, is a finite set of which we calculate the cardinality.

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11

KOCK, JOACHIM. "Tangency quantum cohomology and characteristic numbers." Anais da Academia Brasileira de Ciências 73, no. 3 (September 2001): 319–26. http://dx.doi.org/10.1590/s0001-37652001000300002.

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This work establishes a connection between gravitational quantum cohomology and enumerative geometry of rational curves (in a projective homogeneous variety) subject to conditions of infinitesimal nature like, for example, tangency. The key concept is that of modified psi classes, which are well suited for enumerative purposes and substitute the tautological psi classes of 2D gravity. The main results are two systems of differential equations for the generating function of certain top products of such classes. One is topological recursion while the other is Witten-Dijkgraaf-Verlinde-Verlinde. In both cases, however, the background metric is not the usual Poincaré metric but a certain deformation of it, which surprisingly encodes all the combinatorics of the peculiar way modified psi classes restrict to the boundary. This machinery is applied to various enumerative problems, among which characteristic numbers in any projective homogeneous variety, characteristic numbers for curves with cusp, prescribed triple contact, or double points.

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12

Choudhry, Ajai. "A new method of solving certain quartic and higher degree diophantine equations." International Journal of Number Theory 14, no. 08 (August 22, 2018): 2129–54. http://dx.doi.org/10.1142/s1793042118501282.

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In this paper, we present a new method of solving certain quartic and higher degree homogeneous polynomial diophantine equations in four variables. The method can also be applied to some diophantine systems in five or more variables. Under certain conditions, the method yields an arbitrarily large number of integer solutions of such diophantine equations and diophantine systems, two examples being a sextic equation in four variables and two simultaneous equations of degrees four and six in six variables. We also simultaneously obtain arbitrarily many rational solutions of certain related nonhomogeneous equations of high degree. We obtain these solutions without finding a curve of genus 0 or 1 on the variety defined by the equations concerned. It appears that there exist projective varieties on which there are an arbitrarily large number of rational points and which do not contain a curve of genus 0 or 1 with infinitely many rational points.

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13

KUSTIN, ANDREW R., CLAUDIA POLINI, and BERND ULRICH. "BLOWUPS AND FIBERS OF MORPHISMS." Nagoya Mathematical Journal 224, no. 1 (September 13, 2016): 168–201. http://dx.doi.org/10.1017/nmj.2016.34.

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Our object of study is a rational map defined by homogeneous forms $g_{1},\ldots ,g_{n}$, of the same degree $d$, in the homogeneous coordinate ring $R=k[x_{1},\ldots ,x_{s}]$ of $\mathbb{P}_{k}^{s-1}$. Our goal is to relate properties of $\unicode[STIX]{x1D6F9}$, of the homogeneous coordinate ring $A=k[g_{1},\ldots ,g_{n}]$ of the variety parameterized by $\unicode[STIX]{x1D6F9}$, and of the Rees algebra ${\mathcal{R}}(I)$, the bihomogeneous coordinate ring of the graph of $\unicode[STIX]{x1D6F9}$. For a regular map $\unicode[STIX]{x1D6F9}$, for instance, we prove that ${\mathcal{R}}(I)$ satisfies Serre’s condition $R_{i}$, for some $i>0$, if and only if $A$ satisfies $R_{i-1}$ and $\unicode[STIX]{x1D6F9}$ is birational onto its image. Thus, in particular, $\unicode[STIX]{x1D6F9}$ is birational onto its image if and only if ${\mathcal{R}}(I)$ satisfies $R_{1}$. Either condition has implications for the shape of the core, namely, $\text{core}(I)$ is the multiplier ideal of $I^{s}$ and $\text{core}(I)=(x_{1},\ldots ,x_{s})^{sd-s+1}.$ Conversely, for $s=2$, either equality for the core implies birationality. In addition, by means of the generalized rows of the syzygy matrix of $g_{1},\ldots ,g_{n}$, we give an explicit method to reduce the nonbirational case to the birational one when $s=2$.

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14

KIEM, YOUNG-HOON, and HAN-BOM MOON. "MODULI SPACE OF STABLE MAPS TO PROJECTIVE SPACE VIA GIT." International Journal of Mathematics 21, no. 05 (May 2010): 639–64. http://dx.doi.org/10.1142/s0129167x10006264.

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We compare the Kontsevich moduli space [Formula: see text] of stable maps to projective space with the quasi-map space ℙ( Sym d(ℂ2) ⊗ ℂn)//SL(2). Consider the birational map [Formula: see text] which assigns to an n tuple of degree d homogeneous polynomials f1, …, fn in two variables, the map f = (f1 : ⋯ : fn) : ℙ1 → ℙn-1. In this paper, for d = 3, we prove that [Formula: see text] is the composition of three blow-ups followed by two blow-downs. Furthermore, we identify the blow-up/down centers explicitly in terms of the moduli spaces [Formula: see text] with d = 1, 2. In particular, [Formula: see text] is the SL(2)-quotient of a smooth rational projective variety. The degree two case [Formula: see text], which is the blow-up of ℙ( Sym 2ℂ2 ⊗ ℂn)//SL(2) along ℙn-1, is worked out as a preliminary example.

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15

Hang, Tian, Hui-Jiuan Chen, Shuai Xiao, Chengduan Yang, Meiwan Chen, Jun Tao, Han-ping Shieh, Bo-ru Yang, Chuan Liu, and Xi Xie. "TiO 2 nanowire-templated hierarchical nanowire network as water-repelling coating." Royal Society Open Science 4, no. 12 (December 2017): 171431. http://dx.doi.org/10.1098/rsos.171431.

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Extraordinary water-repelling properties of superhydrophobic surfaces make them novel candidates for a great variety of potential applications. A general approach to achieve superhydrophobicity requires low-energy coating on the surface and roughness on nano- and micrometre scale. However, typical construction of superhydrophobic surfaces with micro-nano structure through top-down fabrication is restricted by sophisticated fabrication techniques and limited choices of substrate materials. Micro-nanoscale topographies templated by conventional microparticles through surface coating may produce large variations in roughness and uncontrollable defects, resulting in poorly controlled surface morphology and wettability. In this work, micro-nanoscale hierarchical nanowire network was fabricated to construct self-cleaning coating using one-dimensional TiO 2 nanowires as microscale templates. Hierarchical structure with homogeneous morphology was achieved by branching ZnO nanowires on the TiO 2 nanowire backbones through hydrothermal reaction. The hierarchical nanowire network displayed homogeneous micro/nano-topography, in contrast to hierarchical structure templated by traditional microparticles. This hierarchical nanowire network film exhibited high repellency to both water and cell culture medium after functionalization with fluorinated organic molecules. The hierarchical structure templated by TiO 2 nanowire coating significantly increased the surface superhydrophobicity compared to vertical ZnO nanowires with nanotopography alone. Our results demonstrated a promising strategy of using nanowires as microscale templates for the rational design of hierarchical coatings with desired superhydrophobicity that can also be applied to various substrate materials.

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16

Ribeiro, William C. O., Vinícius Lobosco, and Patrícia F. M. Martinez. "Solubility parameters analysis of Eucalyptus urograndis kraft lignin." BioResources 15, no. 4 (September 23, 2020): 8577–600. http://dx.doi.org/10.15376/biores.15.4.8577-8600.

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Lignin has gained momentum as a renewable material because it is the largest natural source that can provide aromatic compounds in a wide range of applications. However, its heterogeneity in terms of high polydispersity molar mass distribution and variety of functional groups has limited the direct production of added-value lignin-derivatives. Among the alternatives to obtain more homogeneous lignin cuts is solvent fractionation. However, it is not well understood how different solvents influence lignin partition, and thus it is difficult to establish a rational solvent order to perform it. Thus, the purpose of this work was to understand Eucalyptus urograndis kraft lignin partition in organic solvents through the application of three solubility parameter theories: Hildebrand, Hansen (HSP), and Functional (FSP). Through the theories studied, FSP provided the best representation of lignin partition in organic solvents. In addition, the influence of solvents’ solubility parameters on lignin solubility was investigated by multiregression analyses, which revealed that only the polar solvent parameter showed statistical relevance to describe lignin solubility. The results of this work may contribute to the effective development of technical lignins’ fractionation, allowing the production of higher-value lignin derivatives, increasing the profitability of biorefineries, and establishing a sustainable bio-based economy.

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17

Sarafopoulos, Georges, and Kosmas Papadopoulos. "Chaos in Oligopoly Models." International Journal of Productivity Management and Assessment Technologies 7, no. 1 (January 2019): 50–76. http://dx.doi.org/10.4018/ijpmat.2019010104.

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In this article, the authors investigate the dynamics of two oligopoly games. In the first game, they consider a nonlinear Cournot-type duopoly game with homogeneous goods and same rational expectations. The authors investigate the case, where managers have a variety of attitudes toward relative performance that are indexed by their type. In the second game they consider a Cournot-Bertrand duopoly game with linear demand, quadratic cost function and differentiated goods. In the two games they suppose a linear demand and a quadratic cost function. The games are modeled with a system of two difference equations. Existence and stability of equilibria of the systems are studied. The authors show that the models gives more complex, chaotic and unpredictable trajectories, as a consequence of change in the parameter k of speed of the player's adjustment (in the first game) and in the parameter d of the horizontal product differentiation (in the second game). The authors prove that the variation of the parameter k (resp. d) destabilizes the Nash equilibrium via a period doubling bifurcation (resp. through a Neimark-Sacker bifurcation). The chaotic features are justified numerically via computing Lyapunov numbers and sensitive dependence on initial conditions. In the second game they show that in the case of a quadratic cost there are stable trajectories and a higher or lower degree of product differentiation does not tend to destabilize the economy. They verify these results through numerical simulations. Finally, the authors control the chaotic behavior of the games introducing a new parameter. For some values of this parameter, the Nash equilibrium is stable for every value of the main parameter k or d.

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18

Kikulis, Lisa M., Trevor Slack, Bob Hinings, and Alan Zimmermann. "A Structural Taxonomy of Amateur Sport Organizations." Journal of Sport Management 3, no. 2 (July 1989): 129–50. http://dx.doi.org/10.1123/jsm.3.2.129.

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The theoretical rationale underlying this study was that a variety of structural design types exist in amateur sport organizations and that their structural characteristics may be effectively measured, scaled, and compared. Characteristics were defined along three dimensions of organizational structure: specialization, standardization, and centralization. The approach used to identify the structural design types was the creation of an organizational taxonomy. Based on the measurement of 15 structural scales for 59 provincial sport organizations, Ward’s hierarchical fusion algorithm clustering technique was used to partition these data into homogeneous subsets. Analysis revealed 8 structural design types. The results, while providing support for the idea that there is a trend toward a more professional and bureaucratic form for amateur sport organizations, also suggest that it is important to consider the potential variety in the structural design of these organizations.

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19

Adegbite, Ayobami, and Pumtiwitt C. McCarthy. "Recent and Future Advances in the Chemoenzymatic Synthesis of Homogeneous Glycans for Bacterial Glycoconjugate Vaccine Development." Vaccines 9, no. 9 (September 14, 2021): 1021. http://dx.doi.org/10.3390/vaccines9091021.

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Vaccines are important in preventing disease outbreaks and controlling the spread of disease in a population. A variety of vaccines exist, including subunit, recombinant, and conjugate vaccines. Glycoconjugate vaccines have been an important tool to fight against diseases caused by a number of bacteria. Glycoconjugate vaccines are often heterogeneous. Vaccines of the future are becoming more rationally designed to have a defined oligosaccharide chain length and position of conjugation. Homogenous vaccines could play an important role in assessing the relationship between vaccine structure and immune response. This review focuses on recent advances in the chemoenzymatic production of defined bacterial oligosaccharides for vaccine development with a focus on Neisseria meningitidis and selected WHO-prioritized antibacterial resistant-pathogens. We also provide some perspective on future advances in the chemoenzymatic synthesis of well-defined oligosaccharides.

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20

JELIHOVSCHI, Enio Galinkin, and Cristiano Mauro Assis GOMES. "PROPOSING AN ACHIEVEMENT SIMULATION METHODOLOGY TO ALLOW THE ESTIMATION OF INDIVIDUAL IN CLINICAL TESTING CONTEXT." REVISTA BRASILEIRA DE BIOMETRIA 37, no. 4 (December 20, 2019): 493. http://dx.doi.org/10.28951/rbb.v37i4.423.

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Information from the population should be directly transposed to the individual level only under strict conditions of stationarity and homogeneity. In general, psychological phenomena are neither stationary nor homogeneous. Furthermore, the individual parameters must be estimated. The usual techniques of estimating the individual are rarely attainable. This occurs because in order to get valid estimates of individual parameters, many occasions of the same test must be performed. In this article, we propose an approach (simerg algorithm) to estimate the individual, so that a proper clinical testing for the individual in the context of testing setting that require the respondents' performance becomes viable. We present the rationale of simerg and apply it to estimate the verbal comprehension ability of three individuals, which performed, in 90 different occasions, the 60 items of this ability. In this application, we show how simerg uses the initial empirical performance of these persons and simulates their whole performance. We evaluate the validity of simerg using different measures to predict the empirical performance. We conclude that simerg produces valid estimates. Further studies in a variety of populations and tests that require respondents' performance are needed to enable a stronger conclusion about the validity of simerg.

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21

Hanson, Bonnie J., Justin Wetter, Mark R. Bercher, Leisha Kopp, Maya Fuerstenau-Sharp, Kevin L. Vedvik, Thomas Zielinski, Chris Doucette, Pamela J. Whitney, and Chetana Revankar. "A Homogeneous Fluorescent Live-Cell Assay for Measuring 7-Transmembrane Receptor Activity and Agonist Functional Selectivity Through Beta-Arrestin Recruitment." Journal of Biomolecular Screening 14, no. 7 (June 16, 2009): 798–810. http://dx.doi.org/10.1177/1087057109335260.

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Seven-transmembrane (7TM) receptors play an essential role in the regulation of a wide variety of physiological processes, making them one of the top target classes for pharmaceuticals. 7TM receptor function is mediated and modulated through 2 primary processes: G-protein and beta-arrestin signaling. Classically, it has been recognized that these 2 processes can interact with one another during 7TM receptor desensitization, but it has more recently been recognized that these 2 processes can also act independently of one another and can activate parallel signaling pathways. As such, the methods used to interrogate 7TM receptor signaling, both from a biological and a pharmaceutical perspective, may need to be reevaluated and the question of whether functionally selective compounds (compounds that selectively activate one pathway over another) can be rationally developed must be raised. Although numerous high-throughput screening (HTS) compatible assays exist for studying second messengers arising from G-protein signaling, far fewer HTS compatible assays exist for studying beta-arrestin recruitment. The authors report on the Tango™ 7TM receptor assay technology, a high-throughput homogeneous assay method for monitoring beta-arrestin recruitment that uses a live-cell fluorescent readout. This assay format is broadly applicable to 7TM receptors, independent of G-protein coupling and, as such, has been used to produce assays for over 70 7TM receptor targets. The authors also show how flow cytometry can be used to select clones with desired pharmacological profiles and how an inducible expression system can increase the assay window for targets with high levels of constitutive activity. Finally, they demonstrate how the Tango™ system can be used in parallel with assays aimed at second-messenger signaling to enable functional selectivity studies. ( Journal of Biomolecular Screening 2009:798-810)

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22

Li, Liang, Xuesong Chu, and Guangming Yu. "Cohesive slope failure analysis using methods combining smoothed particle hydrodynamics and response surface function." Engineering Computations 37, no. 3 (November 21, 2019): 1093–108. http://dx.doi.org/10.1108/ec-03-2019-0118.

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Purpose The paper aims to construct a method to simulate the relationship between the parameters of soil properties and the area of sliding mass of the true slip surface of a landslide. Design/methodology/approach The smoothed particle hydrodynamics (SPH) algorithm is used to calibrate a response surface function which is adopted to quantify the area of sliding mass of the true slip surface for each failure sample in Monte Carlo simulation. The proposed method is illustrated through a homogeneous and a heterogeneous cohesive soil slope. Findings The comparison of the results between the proposed method and the traditional method using the slip surface with minimum factor of safety (FSmin) to quantify the failure consequence has shown that the landslide risk tends to be attributed to a variety of risk sources, and that the use of a slip surface with FSmin to quantify the consequence of a landslide underestimates the landslide risk value. The difference of the risk value between the proposed method and the traditional method increases dramatically as the uncertainty of soil properties becomes significant. Practical implications A geotechnical engineer could use the proposed method to perform slope failure analysis. Originality/value The failure consequence of a landslide can be rationally predicted using the proposed method.

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23

DeGroot, Peter B. "Comparison of Dilution Strategies for Dealing with Unanalyzed Elements in X-Ray Fluorescence Analysis." Advances in X-ray Analysis 30 (1986): 175–82. http://dx.doi.org/10.1154/s0376030800021273.

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AbstractOne method of dealing with unanalyzed light elements in x-ray fluorescence analyses is to add a relatively large quantity of a diluent to the sample. The interelement effects on the measured radiation are then essentially all due to the diluent, and the effects of the unanalyzed elements are ignored. The general practice has been to use a diluent compound composed of light elements. The rationale for this is that light elements absorb the analyte radiation less strongly than heavy ones, leaving higher net intensity available after dilution. However, since absorption effects are greater with heavy elements, a smaller dilution factor can be used to reach the analyte concentration at which the effects of unanalyzed elements on the analyte radiation are negligible compared to diluent effects. In many cases, the smaller dilution factor almost exactly compensates for the increased absorption. There is essentially no intensity penalty for using a heavy element diluent. In fact, there are some advantages to doing so. The lower dilution factor with heavy elements can avoid problems with multiple dilutions or accurate weighing and homogeneous blending of very small quantities necessary to achieve high dilution factors. Significantly less continuum radiation is scattered from heavy element matrices, and signal-to-background ratio can be higher in some parts of the spectrum. With high energy analyte lines, heavy element dilution results in infinitely thick samples, simplifying sample preparation. Theoretical intensity calculations using the XRFll matrix correction program are used to predict the appropriate dilution factor for a range of analyte x-ray emission wavelengths with a variety of diluents. The results are verified experimentally.

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24

Dinwiddie, Cynthia L. "The Small-Drillhole Minipermeameter Probe for In-Situ Permeability Measurement." SPE Reservoir Evaluation & Engineering 8, no. 06 (December 1, 2005): 491–501. http://dx.doi.org/10.2118/84595-pa.

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Summary Laboratory measurement of permeability using a Hassler cell is the industry standard; however, consistently removing undisturbed rock samples from friableout crops is difficult. Although various conventional surface-sealing mini-permeameters are developed as an alternative for permeability measurement, these devices generally suffer from difficulties in maintaining optimal forces on the tip seal when dealing with outcrop irregularities in the field; outcrop weathering is also problematic. Because a reliable field method is needed for studies of friable geological units, this paper presents an innovative technique for measuring permeability in situ. The design of the small-drill hole minipermeameter probe is discussed, as well as the accompanying analytical technique and the size and shape of the instrument's averaging volume. Small-diameter holes [i.e., 1.8 cm (0.7 in.)] are drilled into an outcrop with a masonry drill, followed by drillhole vacuuming, probe insertion, sealexpansion, gas injection, and calculation of the intrinsic permeability through measurement of the injection pressure, gas-flow rate, and knowledge of the system geometry. Advantages of this approach include access to a nonweathered surface, an operator-independent sealing mechanism around the air-injection zone, and the potential for permeability measurement at multiple depths below an outcrop surface. To date, data have been collected from four diverse porousmedia: upper and lower shoreface sandstone (Escalante, Utah), saprolitic soils(Clemson, South Carolina), nonwelded and sintered ignimbrite (Bishop, California), and fluvially reworked tuffaceous sedimentary rock (Bishop, California). The probe has proved durable and robust, with a single probe sufficient for making thousands of measurements in a variety of environments. Data quality supports the conclusion that the drillhole probe is a practical field instrument. Introduction Small-scale permeability heterogeneity plays a substantial role in petroleum migration and reservoir performance; this parameter commonly ranges over many orders of magnitude (e.g., 0.01 to more than 10,000 md). Permeability heterogeneities on the meter-to-micrometer scale associated with beds, laminae, internal sedimentary structures, and variations in pore morphology are the source of most retrieval difficulties during enhanced-oil-recovery operations, thus negatively affecting reservoir recovery efficiency. Considerable heterogeneity is evident when permeability measurements are made on small scales, either in the field or on field samples in a laboratory setting. Traditionally, small-scale permeability measurements are made by inducing 1D gas flow through a cylindrical core plug in a Hassler sleeve or cell. Recently, such measurements also are made by inducing multidimensional gas flow through a sample with various configurations of the conventional surface-sealing gas minipermeameter. Cylindrical plugs generally are extracted from continuous core at 30-cmintervals for Hassler-cell permeability measurement, preserving a majority of the core while minimizing associated costs. Except for relatively homogeneous formations, this scale of permeability measurement is in an ill-defined geologic region, falling within the range of laminae and lamina sets. Furthermore, core-plug samples tend to be biased toward the more consolidated, less permeable, and less friable core sections. As an example, the effect of this arbitrary sampling density on Hassler-sleeve measurements for the case of tight gas sands is that magnitudes of permeability less than 100 md frequently result, even when coarser-grained beds that would operate as preferential flow channels or "thief zones" are clearly present. Currently, the scale of sedimentary heterogeneity is best resolved by use of the minipermeameter, which allows investigation of permeability heterogeneity at much greater (and statistically significant) sampling densities and on much smaller scales than is possible with the traditional technique. The literature documents use of the conventional surface-sealing minipermeameter probe for measurements made on outcrop surfaces, core plugs, slabbed cores, or large-cut blocks. One motivation for using cores, plugs, or blocks of rock is that natural weathering processes may greatly affect permeability values obtained from exposed outcrop surfaces. The weathering effect has been shown to extend up to several inches below the rock surface. Beyond the issue of weathering, there are other rationales for discouraging use of the conventional surface-sealing minipermeameter probe in a field setting. When applying this probe geometry to natural rock outcroppings in the field, as opposed to cut specimens in an automated laboratory setting, seal-quality problems are often encountered because of irregular, rough surfaces and difficulties associated with manually holding the probe stationary while applying a uniform normal force of the optimal magnitude on the tip seal. To enable in-situ measurements of friable geologic units and to overcome weathering and seal-quality problems, a new minipermeameter probe has been developed that is specifically intended for application inside a small drilled hole. The design of the small-drillhole minipermeameter probe is discussed in what follows, as well as the accompanying analytical technique and the size and shape of the instrument's averaging volume. This article concludes with brief reviews of data collected using the technique.

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Tsygankov, Alexander S. "History of Philosophy. 2018, Vol. 23, No. 2 TABLE OF CONTENTS Theory and Methodology of History of Philosophy Rodion V. Savinov. Philosophy of Antiquity in Scholasticism This article examines the forms of understanding ancient philosophy in medieval and post-medieval scholasticism. Using the comparative method the author identifies the main approaches to the philosophical heritage of Antiquity, and to the problem of reviving the doctrines of the past. The Patristics (Epiphanius of Cyprus, Filastrius of Brixia, Lactantius, Augustine) saw the ancient cosmological doctrines as heresies. The early Middle Ages (e.g., Isidore of Seville) assimilated the content of these heresiographic treatises, which became the main source of information about ancient philosophy. Scholasticism of the 13th–14th cent. remained cautious to ancient philosophy and distinguished, on the one hand, the doctrinal content discussed in the framework of the exegetic problems at universities (Albert the Great, Thomas Aquinas, etc.), and, on the other hand, information on ancient philosophers integrated into chronological models of medieval chronicles (Peter Comestor, Vincent de Beauvais, Walter Burleigh). Finally, the post-medieval scholasticism (Pedro Fonseca, Conimbricenses, Th. Stanley, and others) raised the questions of the «history of ideas», thereby laying the foundation of the history of philosophy in its modern sense. Keywords: history of philosophy, Patristic, Scholasticism, reflection, critic DOI: 10.21146/2074-5869-2018-23-2-5-17 World Philosophy: the Past and the Present Mariya A. Solopova. The Chronology of Democritus and the Fall of Troy The article considers the chronology of Democritus of Abdera. In the times of Classical Antiquity, three different birth dates for Democritus were known: c. 495 BC (according to Diodorus of Sicily), c. 470 BC (according to Thrasyllus), and c. 460 BC (according to Apollodorus of Athens). These dates must be coordinated with the most valuable doxographic evidence, according to which Democritus 1) "was a young man during Anaxagoras’s old age" and that 2) the Lesser World-System (Diakosmos) was compiled 730 years after the Fall of Troy. The article considers the argument in favor of the most authoritative datings belonging to Apollodorus and Thrasyllus, and draws special attention to the meaning of the dating of Democritus’ work by himself from the year of the Fall of Troy. The question arises, what prompted Democritus to talk about the date of the Fall of Troy and how he could calculate it. The article expresses the opinion that Democritus indicated the date of the Fall of Troy not with the aim of proposing its own date, different from others, but in order to date the Lesser World-System in the spirit of intellectual achievements of his time, in which, perhaps, the history of the development of mankind from the primitive state to the emergence of civilization was discussed. The article discusses how to explain the number 730 and argues that it can be the result of combinations of numbers 20 (the number of generations that lived from the Fall of Troy to Democritus), 35 – one of the constants used for calculations of generations in genealogical research, and 30. The last figure perhaps indicates the age of Democritus himself, when he wrote the Lesser Diakosmos: 30 years old. Keywords: Ancient Greek philosophy, Democritus, Anaxagoras, Greek chronography, doxographers, Apollodorus, Thrasyllus, capture of Troy, ancient genealogies, the length of a generation DOI: 10.21146/2074-5869-2018-23-2-18-31 Bembya L. Mitruyev. “Yogācārabhumi-Śāstra” as a Historical and Philosophical Source The article deals with “Yogācārabhūmi-Śāstra” – a treatise on the Buddhist Yogācāra school. Concerning the authorship of this text, the Indian and Chinese traditions diverge: in the first, the treatise is attributed to Asanga, and in the second tradition to Maitreya. Most of the modern scholars consider it to be a compilation of many texts, and not the work of one author. Being an important monument for both the Yogacara tradition and Mahayana Buddhism in general, Yogācārabhūmi-Śāstra is an object of scientific interest for the researchers all around the world. The text of the treatise consists of five parts, which are divided into chapters. The contents of the treatise sheds light on many concepts of Yogācāra, such as ālayavijñāna, trisvabhāva, kliṣṭamanas, etc. Having briefly considered the textological problems: authorship, dating, translation, commenting and genre of the text, the author suggests the reconstruction of the content of the entire monument, made on the basis of his own translation from the Tibetan and Sanskrit. This allows him to single out from the whole variety of topics those topics, the study of which will increase knowledge about the history of the formation of the basic philosophical concepts of Yogācāra and thereby allow a deeper understanding of the historical and philosophical process in Buddhism and in other philosophical movements of India. Keywords: Yogācārabhūmi-śāstra, Asaṅga, Māhāyana, Vijñānavāda, Yogācāra, Abhidharma, ālayavijñāna citta, bhūmi, mind, consciousness, meditation DOI: 10.21146/2074-5869-2018-23-2-32-43 Tatiana G. Korneeva. Knowledge in Nāșir Khusraw’s Philosophy The article deals with the concept of “knowledge” in the philosophy of Nāșir Khusraw. The author analyzes the formation of the theory of knowledge in the Arab-Muslim philosophy. At the early stages of the formation of the Arab-Muslim philosophy the discussion of the question of cognition was conducted in the framework of ethical and religious disputes. Later followers of the Falsafa introduced the legacy of ancient philosophers into scientific circulation and began to discuss the problems of cognition in a philosophical way. Nāșir Khusraw, an Ismaili philosopher of the 11th century, expanded the scope of knowledge and revised the goals and objectives of the process of cognition. He put knowledge in the foundation of the world order, made it the cause and ultimate goal of the creation of the world. In his philosophy knowledge is the link between the different levels of the universe. The article analyzes the Nāșir Khusraw’s views on the role of knowledge in various fields – metaphysics, cosmogony, ethics and eschatology. Keywords: knowledge, cognition, Ismailism, Nāșir Khusraw, Neoplatonism, Arab-Muslim philosophy, kalām, falsafa DOI: 10.21146/2074-5869-2018-23-2-44-55 Vera Pozzi. Problems of Ontology and Criticism of the Kantian Formalism in Irodion Vetrinskii’s “Institutiones Metaphysicae” (Part II) This paper is a follow-up of the paper «Irodion Vetrinskii’s “Institutiones Metaphysicae” and the St. Petersburg Theological Academy» (Part I). The issue and the role of “ontology” in Vetrinskii’s textbook is analyzed in detail, as well as the author’s critique of Kantian “formalism”: in this connection, the paper provides a description of Vetrinskii’s discussion about Kantian theory of the a priori forms of sensible intuition and understanding. To sum up, Vetrinskii was well acquainted not only with Kantian works – and he was able to fully evaluate their innovative significance – but also with late Scholastic textbooks of the German area. Moreover, he relied on the latters to build up an eclectic defense of traditional Metaphysics, avoiding at the same time to refuse Kantian perspective in the sake of mere reaffirming a “traditional” perspective. Keywords: Philosophizing at Russian Theological Academies, Russian Enlightenment, Russian early Kantianism, St. Petersburg Theological Academy, history of Russian philosophy, history of metaphysics, G.I. Wenzel, I. Ya. Vetrinskii DOI: 10.21146/2074-5869-2018-23-2-56-67 Alexey E. Savin. Criticism of Judaism in Hegel's Early “Theological” Writings The aim of the article is to reveal the nature of criticism of Judaism by the “young” Hegel and underlying intuitions. The investigation is based on the phenomenological approach. It seeks to explicate the horizon of early Hegel's thinking. The revolutionary role of early Hegel’s ideas reactivation in the history of philosophy is revealed. The article demonstrates the fundamental importance of criticism of Judaism for the development of Hegel's thought. The sources of Hegelian thematization and problematization of Judaism – his Protestant theological background within the framework of supranaturalism and the then discussion about human rights and political emancipation of Jews – are discovered. Hegel's interpretation of the history of the Jewish people and the origin of Judaism from the destruction of trust in nature, the fundamental mood of distrust and fear of the world, leading to the development of alienation, is revealed. The falsity of the widespread thesis about early Hegel’s anti-Semitism is demonstrated. The reasons for the transition of early Hegel from “theology” to philosophy are revealed. Keywords: Hegel, Judaism, history, criticism, anti-Semitism, trust, nature, alienation, tyranny, philosophy DOI: 10.21146/2074-5869-2018-23-2-68-80 Evgeniya A. Dolgova. Philosophy at the Institute of Red Professors (1921–1938): Institutional Forms, Methods of Teaching, Students, Lecturers The article explores the history of the Institute of the Red Professors in philosophy (1921–1938). Referring to the unpublished documents in the State Archives of the Russian Federation and the Archive of the Russian Academy of Sciences, the author explores its financial and infrastructure support, information sphere, characterizes students and teachers. The article illustrates the practical experience of the functioning of philosophy within the framework of one of the extraordinary “revolutionary” projects on the renewal of the scientific and pedagogical sphere, reflects a vivid and ambiguous picture of the work of the educational institution in the 1920s and 1930s and corrects some of historiographical judgments (about the politically and socially homogeneous composition of the Institute of Red Professors, the specifics of state support of its work, privileges and the social status of the “red professors”). Keywords: Institute of the Red Professors in Philosophy, Philosophical Department, soviet education, teachers, students, teaching methods DOI: 10.21146/2074-5869-2018-23-2-81-94 Vladimir V. Starovoitov. K. Horney about the Consequences of Neurotic Development and the Ways of Its Overcoming This article investigates the views of Karen Horney on psychoanalysis and neurotic development of personality in her last two books: “Our Inner Conflicts” (1945) and “Neurosis and Human Grows” (1950), and also in her two articles “On Feeling Abused” (1951) and “The Paucity of Inner Experiences” (1952), written in the last two years of her life and summarizing her views on clinical and theoretical problems in her work with neurotics. If in her first book “The Neurotic Personality of Our Time” (1937) neurosis was a result of disturbed interpersonal relations, caused by conditions of culture, then the concept of the idealized Self open the gates to the intrapsychic life. Keywords: Neo-Freudianism, psychoanalysis, neurotic development of personality, real Self, idealized image of Self DOI: 10.21146/2074-5869-2018-23-2-95-102 Publications and Translations Victoria G. Lysenko. Dignāga on the Definition of Perception in the Vādaviddhi of Vasubandhu. A Historical and Philosophical Reconstruction of Dignāga’s Pramāṇasamuccayavṛtti (1.13-16) The paper investigates a fragment from Dignāga’s magnum opus Pramāṇasamuccayavṛtti (“Body of tools for reliable knowledge with a commentary”, 1, 13-16) where Dignāga challenges Vasubandhu’s definition of perception in the Vādaviddhi (“Rules of the dispute”). The definition from the Vādaviddhi is being compared in the paper with Vasubandhu’s ideas of perception in Abhidharmakośabhāṣya (“Encyclopedia of Abhidharma with the commentary”), and with Dignāga’s own definition of valid perception in the first part of his Pramāṇasamuccayavṛtti as well as in his Ālambanaparīkśavṛtti (“Investigation of the Object with the commentary”). The author puts forward the hypothesis that Dignāga criticizes the definition of perception in Vādaviddhi for the reason that it does not correspond to the teachings of Vasubandhu in his Abhidharmakośabhāṣya, to which he, Dignāga, referred earlier in his magnum opus. This helps Dignāga to justify his statement that Vasubandhu himself considered Vādaviddhi as not containing the essence of his teaching (asāra). In addition, the article reconstructs the logical sequence in Dignāga’s exegesis: he criticizes the Vādaviddhi definition from the representational standpoint of Sautrāntika school, by showing that it does not fulfill the function prescribed by Indian logic to definition, that of distinguishing perception from the classes of heterogeneous and homogeneous phenomena. Having proved the impossibility of moving further according to the “realistic logic” based on recognizing the existence of an external object, Dignāga interprets the Vādaviddhi’s definition in terms of linguistic philosophy, according to which the language refers not to external objects and not to the unique and private sensory experience (svalakṣaṇa-qualia), but to the general characteristics (sāmānya-lakṣaṇa), which are mental constructs (kalpanā). Keywords: Buddhism, linguistic philosophy, perception, theory of definition, consciousness, Vaibhashika, Sautrantika, Yogacara, Vasubandhu, Dignaga DOI: 10.21146/2074-5869-2018-23-2-103-117 Elizaveta A. Miroshnichenko. Talks about Lev N. Tolstoy: Reception of the Writer's Views in the Public Thought of Russia at the End of the 19th Century (Dedicated to the 190th Anniversary of the Great Russian Writer and Thinker) This article includes previously unpublished letters of Russian social thinkers such as N.N. Strakhov, E.M. Feoktistov, D.N. Tsertelev. These letters provide critical assessment of Lev N. Tolstoy’s teachings. The preface to publication includes the history of reception of Tolstoy’s moral and aesthetic philosophy by his contemporaries, as well as influence of his theory on the beliefs of Russian idealist philosopher D.N. Tsertelev. The author offers a rational reconstruction of the dialogue between two generations of thinkers representative of the 19th century – Lev N. Tolstoy and N.N. Strakhov, on the one hand, and D.N. Tsertelev, on the other. The main thesis of the paper: the “old” and the “new” generations of the 19th-century thinkers retained mutual interest and continuity in setting the problems and objectives of philosophy, despite the numerous worldview contradictions. Keywords: Russian philosophy of the nineteenth century, L.N. Tolstoy, N.N. Strakhov, D.N. Tsertelev, epistolary heritage, ethics, aesthetics DOI: 10.21146/2074-5869-2018-23-2-118-130 Reviews Nataliya A. Tatarenko. History of Philosophy in a Format of Lecture Notes (on Hegel G.W.F. Vorlesungen zur Ästhetik. Vorlesungsmitschrift Adolf Heimann (1828/1829). Hrsg. von A.P. Olivier und A. Gethmann-Siefert. München: Wilhelm Fink, 2017. XXXI + 254 S.) Released last year, the book “G.W.F. Hegel. Vorlesungen zur Ästhetik. Vorlesungsmitschrift Adolf Heimann (1828/1829)” in German is a publication of one of the student's manuskript of Hegel's lectures on aesthetics. Adolf Heimann was a student of Hegel in 1828/29. These notes open for us imaginary doors into the audience of the Berlin University, where Hegel read his fourth and final course on the philosophy of art. A distinctive feature of this course is a new structure of lectures in comparison with three previous courses. This three-part division was took by H.G. Hotho as the basis for the edited by him text “Lectures on Aesthetics”, included in the first collection of Hegel’s works. The content of that publication was mainly based on the lectures of 1823 and 1826. There are a number of differences between the analyzed published manuskript and the students' records of 1820/21, 1823 and 1826, as well as between the manuskript and the editorial version of H.G. Hotho. These features show that Hegel throughout all four series of Berlin lectures on the philosophy of art actively developed and revised the structure and content of aesthetics. But unfortunately this evidence of the permanent development was not taken into account by the first editor of Hegel's lectures on aesthetics. Keywords: G.W.F. Hegel, H.G. Hotho, philosophy of art, aesthetics, forms of art, idea of beauty, ideal DOI: 10.21146/2074-5869-2018-23-2-131-138 Alexander S. Tsygankov. On the Way to the Revival of Metaphysics: S.L. Frank and E. Coreth Readers are invited to review the monograph of the modern German researcher Oksana Nazarova “The problem of the renaissance and new foundation of metaphysics through the example of Christian philosophical tradition. Russian religious philosophy (Simon L. Frank) and German neosholastics (Emerich Coreth)”, which was published in 2017 in Munich. In the paper, the author offers a comparative analysis of the projects of a new, “post-dogmatic” metaphysics, which were developed in the philosophy of Frank and Coreth. This study addresses the problems of the cognitive-theoretical and ontological foundation of the renaissance of metaphysics, the methodological tools of the new metaphysics, as well as its anthropological component. O. Nazarova's book is based on the comparative analysis of Frank's religious philosophy and Coreth's neo-cholastic philosophy from the beginning to the end. This makes the study unique in its own way. Since earlier in the German reception of the heritage of Russian thinker, the comparison of Frank's philosophy with the Catholic theology of the 20th century was realized only fragmentarily and did not act as a fundamental one. Along with a deep and meaningful analysis of the metaphysical projects of both thinkers, this makes O. Nazarova's book relevant to anyone who is interested in the philosophical dialogue of Russia and Western Europe and is engaged in the work of Frank and Coreth. Keywords: the renaissance of metaphysics, post-Kantian philosophy, Christian philosophy, S.L. Frank, E. Coreth DOI: 10.21146/2074-5869-2018-23-2-139-147". History of Philosophy 23, № 2 (жовтень 2018): 139–47. http://dx.doi.org/10.21146/2074-5869-2018-23-2-139-147.

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Schmitz, David, and Henrik Seppänen. "On the polyhedrality of global Okounkov bodies." Advances in Geometry 16, no. 1 (January 1, 2016). http://dx.doi.org/10.1515/advgeom-2015-0042.

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AbstractWe prove that the existence of a finite Minkowski basis for Okounkov bodies on a smooth projective variety with respect to an admissible flag implies the rational polyhedrality of the global Okounkov body. As an application of this general result, we deduce that the global Okounkov body of a surface with finitely generated pseudo-effective cone with respect to a general flag is rational polyhedral. We give an alternative proof for this fact which recovers the generators more explicitly. We also prove the rational polyhedrality of global Okounkov bodies in the case of certain homogeneous 3-folds using inductive methods.

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Feller, Peter, and Immanuel van Santen. "Existence of embeddings of smooth varieties into linear algebraic groups." Journal of Algebraic Geometry, October 3, 2022. http://dx.doi.org/10.1090/jag/793.

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We prove that every smooth affine variety of dimension d d embeds into every simple algebraic group of dimension at least 2 d + 2 2d+2 . We do this by establishing the existence of embeddings of smooth affine varieties into the total space of certain principal bundles. For the latter we employ and build upon parametric transversality results for flexible affine varieties due to Kaliman. By adapting a Chow-group-based argument due to Bloch, Murthy, and Szpiro, we show that our result is optimal up to a possible improvement of the bound to 2 d + 1 2d+1 . In order to study the limits of our embedding method, we use rational homology group calculations of homogeneous spaces and we establish a domination result for rational homology of complex smooth varieties.

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Franceschini, Alberto. "Minimal bandwidth for $${\mathbb C}^*$$-actions on generalized Grassmannians." Rendiconti del Circolo Matematico di Palermo Series 2, June 4, 2022. http://dx.doi.org/10.1007/s12215-022-00745-8.

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AbstractThe bandwidth of a $${\mathbb C}^*$$ C ∗ -action of a polarized pair (X, L) is a natural measure of its complexity. In this paper, we study $${\mathbb C}^*$$ C ∗ -actions on rational homogeneous spaces, determining which provide minimal bandwidth. We prove that the minimal bandwidth is linked to the smallest coefficient of the fundamental weight, in a base of simple roots, which describes the variety as a marked Dynkin diagram. As a direct application of the results we study the Chow groups of the Cayley plane $$\mathrm{E}_6(6)$$ E 6 ( 6 ) .

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Yoo, Sungjae, Jeongwon Kim, Sungwoo Choi, Doojae Park, and Sungho Park. "Two-dimensional nanoframes with dual rims." Nature Communications 10, no. 1 (December 2019). http://dx.doi.org/10.1038/s41467-019-13738-6.

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AbstractThe synthesis of highly complex two-dimensional (2D) metal nanoframes remains a great challenge. Synthetic strategies for preparing 2D metal nanoframes are few, and rational and systematic synthetic pathways to more complicated architectures have not yet been reported. Herein, we demonstrate a stepwise synthetic strategy for complex 2D metal nanoframes with a high degree of intricacy; the strategy leads to a variety of shapes, including rings, triangles, hexagons, and tripods with tailorable single or double frames in a single entity. These nanoframes of high homogeneity could be obtained through selective combination of four different chemical toolkits consisting of selective etching and deposition on certain facets, and concentric and/or eccentric regrowth by controlling the mismatches of lattice constants of metals. The resulting nanoframes were highly homogeneous in size and shape and had van der Waals interactions that maximized rim-to-rim contact, allowing them to uniquely self-assemble into large-area superstructures.

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Strofaldi, Alessandro, Michelle K. Quinn, Annela Seddon, and Jennifer McManus. "Polymorphic protein phase transitions driven by surface anisotropy." Journal of Chemical Physics, December 12, 2022. http://dx.doi.org/10.1063/5.0125452.

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Phase transitions of proteins are strongly influenced by surface chemical modifications or mutations. Human γD-crystallin (HGD) single-mutants have been extensively studied due to their association with juvenile cataract. However, they have also provided a rich library of molecules to examine how specific inter-protein interactions direct protein assembly, providing new insights and valuable experimental data for coarse-grained patchy-particle models. Here we demonstrate that the addition of new inter-protein interactions by mutagenesis is additive and increases the number and variety of condensed phases formed by proteins. When double mutations incorporating two specific point mutations are made, the properties of both are retained in addition to the formation a new condensed phase. We find that the HGD double-mutant P23VC110M self-assembles into spherical particles with retrograde solubility, orthorhombic crystals and needle/plate shape crystals, while retaining the ability to undergo liquid-liquid phase separation. This rich polymorphism is only partially predicted by the experimental data on the constituent single mutants. We also report a previously un-characterized amorphous protein particle, with unique properties that differ from those of protein spherulites and protein particulates previously described. The particles are amorphous, reversible with temperature, tens of microns in size and perfectly spherical. When they are grown on pristine surfaces, they appear to form by homogeneous nucleation making them unique, and possibly a new form of protein condensate. This work highlights the challenges in predicting protein behaviour, which has frustrated rational assembly and crystallization, but also provides rich data to develop new coarse-grained models to explain the observed polymorphism.

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Maqbool, Masrat, and Wani A. Ahad. "Characterization and Classification of High Density Apple Orchard Soils of North Kashmir." Journal of Experimental Agriculture International, April 9, 2022, 13–30. http://dx.doi.org/10.9734/jeai/2022/v44i430812.

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Jammu & Kashmir presents a benefit for the economy of India, since is the rich producer of fruits and vegetables and is the most important temperate fruit producing state. Apple is the oldest and commercially the most important temperate fruit and is the fourth among the most widely produced fruit. Basic needs of life can be fulfilled by maintaining high productivity of soil and having the rational use of soil as per its potentiality in order to maintain sustainability. At the same time, the sustainable use of soil resource requires extensive knowledge regarding its genesis, morphology and other properties. Despite the importance of the area for producing quality apples, high density apple were planted in 2002. However no systematic study was undertaken so far with respect to soil characterization and classification of apple orchard soils under high density plantation. Keeping all this in view, the present investigation entitled, “Characterization and classification of High Density Apple Orchard Soils of North Kashmir” was undertaken . current paper aims to contribute to the existing challenge in soil research in India. To this end 45 soil profiles were observed in orchards,- Based on homogeneous properties, e.g., age, topography, rootstock, variety only 12 profiles were selected from 45 observed profiles (purposive method of sampling). These twelve profiles were categorized into high, mid and low altitudes for detailed investigation of the soil profile properties and to classify soils of the district as per Keys to Soil Taxonomy (2015). The excavated soil profiles were exposed to a depth of 120 cm and more for studying morphological and physico-chemical characteristics. As per the results, profiles of the study area were classified from ‘ moderately deep’ to ‘very deep. A slight strong effervescence with diluted HCl was observed both in surface and sub-surface horizons profile P3, P7 and P10 located especially in mid and low altitude. The pH were ranging between 6.60 to 8.10 in the surface horizons whereas in the sub surface horizons it ranged from 6.84 to 8.50 and showed an increasing trend with depth. The EC in general showed increasing trend with depth as compared to surface horizons and was found to be in normal range in both horizons. On the basis of the U.S. Comprehensive System of Soil Classification as per Keys to Soil Taxonomy (Soil Survey Staff, 2014) and Soil Survey Manual (Soil Survey Staff, 2003), studied profiles were placed in the orders of Mollisols, Alfisols, Inceptisols and Entisols and the suborders Udolls, Udalfs, Orchrepts and Orthents. The great groups to which these soils were further classified are Argiudolls, Hapludalfs, Eutrochrepts and Udorthents respectively, on the basis of presence of the diagnostic surface and sub-surface horizons, profile development and the presence of particular moisture and temperature regime. However this study was first of its kind with an aim to evaluate the most probable path of plant nutrients added to soil. In this way, it can also support a better understanding of the soil genesis and the electro-chemical behavior. Besides, detailed study of clay mineralogy may provide a tool to classify the soils up to series level.

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