Journal articles: 'Hawkesbury (N.S.W.)'

1

Bousquet, Pierre. "Topological singularities in W S,P (S N , S 1)." Journal d'Analyse Mathématique 102, no. 1 (August 2007): 311–46. http://dx.doi.org/10.1007/s11854-007-0023-z.

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Roesky, Herbert W., Michael Zimmer, Regine Herbst, and George M. Sheldrick. "N,N′-Bis(diphenyIphosphino)-S,S-dimethylsulfodiimin – ein Ligand für cyclische Übergangsmetallkomplexe/ N,N′-Bis(diphenylphosphino)-S,S-dimethylsulfodiimine – a Ligand for Cyclic Transition Metal Complexes." Zeitschrift für Naturforschung B 43, no. 8 (August 1, 1988): 933–36. http://dx.doi.org/10.1515/znb-1988-0802.

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AbstractMe2SN2P2Ph4M(CO)4 complexes (1) (M: 1 a Cr, 1 b Mo, 1 c W) have been synthesized from Me2S(NPPh2)2 and C7H8M(CO)4 . 1a-1c are stable at room temperature, 1 b crystallizes in the space group P21212 with cell constants a = 2486.3(2); b = 1488.8(1); c = 882.0(1) pm.

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Mackay, MF, PJ Oliver, and CG Young. "Synthesis and X-Ray Structure of syn-Di-μ-thio-bis[(N,N-diethyldithiocarbamato-S,S')oxotungsten(V)]." Australian Journal of Chemistry 42, no. 6 (1989): 837. http://dx.doi.org/10.1071/ch9890837.

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The reaction of WSCl4 and Me3SiS2CNEt2 in tetrahydrofuran produces a green solid which yields WS(S2)(S2CNEt2)2, WO(S2)(S2CNEt2)2 and syn-W2O2( �-S)2(S2CNEt2)2 upon exposure to oxygen. Crystals of syn-W2O2( �-S)2(S2CNEt2)2 are monoclinic and belong to space group C2/c with a 33.880(4), b 7.012(1), c 18.072(1) � ,β 105.94(1)� and Z 8. Refinement on 2651 data measured with Cu K α: radiation converged at R 0.070. The complex possesses a syn-[W2O2(�-S)2]2+ core with a W-W bond [2.808(1) � ] and two terminal W-O bonds [1.66(2) and 1.68(2) � ]. The W-S(bridging) bond distances are in the range 2.319(5)-2.3346) � Each of the square-pyramidal tungsten atoms is further coordinated to a bidentate dithiocarbamate ligand with W-S bond distances ranging from 2.447(6) to 2.459(5) � .

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BERGSHOEFF, E., and M. DE ROO. "N=2 W SUPERGRAVITY." International Journal of Modern Physics A 08, no. 02 (January 20, 1993): 237–76. http://dx.doi.org/10.1142/s0217751x93000102.

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We quantize the classical gauge theory of N=2 w∞ supergravity and show how the underlying N=2 super-w∞ algebra gets deformed into an N=2 super-W∞ algebra. Both algebras contain the N=2 super-Virasoro algebra as a subalgebra. We discuss how one can extract from these results information about quantum N=2 WN supergravity theories containing a finite number of higher-spin symmetries with superspin s≤N. As an example we discuss the case of quantum N=2 W3 supergravity.

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Sun, Zhi-Wei. "On the Function w ( x )=|{1= s = k : x = a s (mod n s )}|." Combinatorica 23, no. 4 (December 1, 2003): 681–91. http://dx.doi.org/10.1007/s00493-003-0041-0.

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Nossa, A., and A. Cavaleiro. "Mechanical behaviour of W–S–N and W–S–C sputtered coatings deposited with a Ti interlayer." Surface and Coatings Technology 163-164 (January 2003): 552–60. http://dx.doi.org/10.1016/s0257-8972(02)00622-9.

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Sonoda, Kenji. "W. S. Lewis and N. Murakami eds., Ranald MacDonald." Historical English Studies in Japan, no. 22 (1989): 33–45. http://dx.doi.org/10.5024/jeigakushi.1990.33.

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Ticha, I. "Erhardt, W., Gotz, E., Bodeker, N., Seybold, S.: ZANDER." Biologia plantarum 44, no. 1 (March 1, 2001): 82. http://dx.doi.org/10.1023/a:1017984102467.

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Gustavsson, Fredrik, Staffan Jacobson, Albano Cavaleiro, and Tomas Polcar. "Ultra-low friction W–S–N solid lubricant coating." Surface and Coatings Technology 232 (October 2013): 541–48. http://dx.doi.org/10.1016/j.surfcoat.2013.06.026.

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Nossa, A., and A. Cavaleiro. "Tribological Behaviour of N(C)-Alloyed W–S Films." Tribology Letters 28, no. 1 (July 20, 2007): 59–70. http://dx.doi.org/10.1007/s11249-007-9248-3.

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Mullins, D. R., P. F. Lyman, and S. H. Overbury. "Interaction of S with W(001)." Surface Science Letters 277, no. 1-2 (October 1992): A35. http://dx.doi.org/10.1016/0167-2584(92)90117-n.

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12

Soares, Louis. "Hecke Triangle Groups, Transfer Operators and Hausdorff Dimension." Annales Henri Poincaré 23, no. 4 (October 4, 2021): 1239–81. http://dx.doi.org/10.1007/s00023-021-01117-1.

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AbstractWe consider the family of Hecke triangle groups $$ \Gamma _{w} = \langle S, T_w\rangle $$ Γ w = ⟨ S , T w ⟩ generated by the Möbius transformations $$ S : z\mapsto -1/z $$ S : z ↦ - 1 / z and $$ T_{w} : z \mapsto z+w $$ T w : z ↦ z + w with $$ w > 2.$$ w > 2 . In this case, the corresponding hyperbolic quotient $$ \Gamma _{w}\backslash {\mathbb {H}}^2 $$ Γ w \ H 2 is an infinite-area orbifold. Moreover, the limit set of $$ \Gamma _w $$ Γ w is a Cantor-like fractal whose Hausdorff dimension we denote by $$ \delta (w). $$ δ ( w ) . The first result of this paper asserts that the twisted Selberg zeta function $$ Z_{\Gamma _{ w}}(s, \rho ) $$ Z Γ w ( s , ρ ) , where $$ \rho : \Gamma _{w} \rightarrow \mathrm {U}(V) $$ ρ : Γ w → U ( V ) is an arbitrary finite-dimensional unitary representation, can be realized as the Fredholm determinant of a Mayer-type transfer operator. This result has a number of applications. We study the distribution of the zeros in the half-plane $$\mathrm {Re}(s) > \frac{1}{2}$$ Re ( s ) > 1 2 of the Selberg zeta function of a special family of subgroups $$( \Gamma _w^N )_{N\in {\mathbb {N}}} $$ ( Γ w N ) N ∈ N of $$\Gamma _w$$ Γ w . These zeros correspond to the eigenvalues of the Laplacian on the associated hyperbolic surfaces $$X_w^N = \Gamma _w^N \backslash {\mathbb {H}}^2$$ X w N = Γ w N \ H 2 . We show that the classical Selberg zeta function $$Z_{\Gamma _w}(s)$$ Z Γ w ( s ) can be approximated by determinants of finite matrices whose entries are explicitly given in terms of the Riemann zeta function. Moreover, we prove an asymptotic expansion for the Hausdorff dimension $$\delta (w)$$ δ ( w ) as $$w\rightarrow \infty $$ w → ∞ .

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Soares, Louis. "Hecke Triangle Groups, Transfer Operators and Hausdorff Dimension." Annales Henri Poincaré 23, no. 4 (October 4, 2021): 1239–81. http://dx.doi.org/10.1007/s00023-021-01117-1.

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AbstractWe consider the family of Hecke triangle groups $$ \Gamma _{w} = \langle S, T_w\rangle $$ Γ w = ⟨ S , T w ⟩ generated by the Möbius transformations $$ S : z\mapsto -1/z $$ S : z ↦ - 1 / z and $$ T_{w} : z \mapsto z+w $$ T w : z ↦ z + w with $$ w > 2.$$ w > 2 . In this case, the corresponding hyperbolic quotient $$ \Gamma _{w}\backslash {\mathbb {H}}^2 $$ Γ w \ H 2 is an infinite-area orbifold. Moreover, the limit set of $$ \Gamma _w $$ Γ w is a Cantor-like fractal whose Hausdorff dimension we denote by $$ \delta (w). $$ δ ( w ) . The first result of this paper asserts that the twisted Selberg zeta function $$ Z_{\Gamma _{ w}}(s, \rho ) $$ Z Γ w ( s , ρ ) , where $$ \rho : \Gamma _{w} \rightarrow \mathrm {U}(V) $$ ρ : Γ w → U ( V ) is an arbitrary finite-dimensional unitary representation, can be realized as the Fredholm determinant of a Mayer-type transfer operator. This result has a number of applications. We study the distribution of the zeros in the half-plane $$\mathrm {Re}(s) > \frac{1}{2}$$ Re ( s ) > 1 2 of the Selberg zeta function of a special family of subgroups $$( \Gamma _w^N )_{N\in {\mathbb {N}}} $$ ( Γ w N ) N ∈ N of $$\Gamma _w$$ Γ w . These zeros correspond to the eigenvalues of the Laplacian on the associated hyperbolic surfaces $$X_w^N = \Gamma _w^N \backslash {\mathbb {H}}^2$$ X w N = Γ w N \ H 2 . We show that the classical Selberg zeta function $$Z_{\Gamma _w}(s)$$ Z Γ w ( s ) can be approximated by determinants of finite matrices whose entries are explicitly given in terms of the Riemann zeta function. Moreover, we prove an asymptotic expansion for the Hausdorff dimension $$\delta (w)$$ δ ( w ) as $$w\rightarrow \infty $$ w → ∞ .

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Akutagawa, Kazuo. "An Obata-type theorem on compact Einstein manifolds with boundary." Geometriae Dedicata 213, no. 1 (February 3, 2021): 577–87. http://dx.doi.org/10.1007/s10711-021-00598-y.

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AbstractWe show a kind of Obata-type theorem on a compact Einstein n-manifold $$(W, \bar{g})$$ ( W , g ¯ ) with smooth boundary $$\partial W$$ ∂ W . Assume that the boundary $$\partial W$$ ∂ W is minimal in $$(W, \bar{g})$$ ( W , g ¯ ) . If $$(\partial W, \bar{g}|_{\partial W})$$ ( ∂ W , g ¯ | ∂ W ) is not conformally diffeomorphic to $$(S^{n-1}, g_S)$$ ( S n - 1 , g S ) , then for any Einstein metric $$\check{g} \in [\bar{g}]$$ g ˇ ∈ [ g ¯ ] with the minimal boundary condition, we have that, up to rescaling, $$\check{g} = \bar{g}$$ g ˇ = g ¯ . Here, $$g_S$$ g S and $$[\bar{g}]$$ [ g ¯ ] denote respectively the standard round metric on the $$(n-1)$$ ( n - 1 ) -sphere $$S^{n-1}$$ S n - 1 and the conformal class of $$\bar{g}$$ g ¯ . Moreover, if we assume that $$\partial W \subset (W, \bar{g})$$ ∂ W ⊂ ( W , g ¯ ) is totally geodesic, we also show a Gursky-Han type inequality for the relative Yamabe constant of $$(W, \partial W, [\bar{g}])$$ ( W , ∂ W , [ g ¯ ] ) .

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Yuldashev, Tursun K., and Farhod G. Mukhamadiev. "THE LOCAL DENSITY AND THE LOCAL WEAK DENSITY IN THE SPACE OF PERMUTATION DEGREE AND IN HATTORI SPACE." Ural Mathematical Journal 6, no. 2 (December 26, 2020): 108. http://dx.doi.org/10.15826/umj.2020.2.011.

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In this paper, the local density $(l d)$ and the local weak density $(l w d)$ in the space of permutation degree as well as the cardinal and topological properties of Hattori spaces are studied. In other words, we study the properties of the functor of permutation degree $S P^{n}$ and the subfunctor of permutation degree $S P_{G}^{n}$, $P$ is the cardinal number of topological spaces. Let $X$ be an infinite $T_{1}$-space. We prove that the following propositions hold.(1) Let $Y^{n} \subset X^{n}$; (A) if $d\, \left(Y^{n} \right)=d\, \left(X^{n} \right)$, then $d\, \left(S P^{n} Y\right)=d\, \left(SP^{n} X\right)$; (B) if $l w d\, \left(Y^{n} \right)=l w d\, \left(X^{n} \right)$, then $l w d\, \left(S P^{n} Y\right)=l w d\, \left(S P^{n} X\right)$. (2) Let $Y\subset X$; (A) if $l d \,(Y)=l d \,(X)$, then $l d\, \left(S P^{n} Y\right)=l d\, \left(S P^{n} X\right)$; (B) if $w d \,(Y)=w d \,(X)$, then $w d\, \left(S P^{n} Y\right)=w d\, \left(S P^{n} X\right)$.(3) Let $n$ be a positive integer, and let $G$ be a subgroup of the permutation group $S_{n}$. If $X$ is a locally compact $T_{1}$-space, then $S P^{n} X, \, S P_{G}^{n} X$, and $\exp _{n} X$ are $k$-spaces.(4) Let $n$ be a positive integer, and let $G$ be a subgroup of the permutation group $S_{n}$. If $X$ is an infinite $T_{1}$-space, then $n \,\pi \,w \left(X\right)=n \, \pi \,w \left(S P^{n} X \right)=n \,\pi \,w \left(S P_{G}^{n} X \right)=n \,\pi \,w \left(\exp _{n} X \right)$.We also have studied that the functors $SP^{n},$ $SP_{G}^{n} ,$ and $\exp _{n} $ preserve any $k$-space. The functors $SP^{2}$ and $SP_{G}^{3}$ do not preserve Hattori spaces on the real line. Besides, it is proved that the density of an infinite $T_{1}$-space $X$ coincides with the densities of the spaces $X^{n}$, $\,S P^{n} X$, and $\exp _{n} X$. It is also shown that the weak density of an infinite $T_{1}$-space $X$ coincides with the weak densities of the spaces $X^{n}$, $\,S P^{n} X$, and $\exp _{n} X$.

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16

Journal, Baghdad Science. "S-maximal Submodules." Baghdad Science Journal 12, no. 1 (March 1, 2015): 210–20. http://dx.doi.org/10.21123/bsj.12.1.210-220.

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Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ? W ? M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of rings and modules. .

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Wei, Zhu, Qingcheng Zhang, Yongzheng Zhang, and Chunyue Wang. "Simple Modules for Modular Lie SuperalgebrasW(0∣n),S(0∣n), andK(n)." Advances in Mathematical Physics 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/250570.

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This paper constructs a series of modules from modular Lie superalgebrasW(0∣n),S(0∣n), andK(n)over a field of prime characteristicp≠2. Cartan subalgebras, maximal vectors of these modular Lie superalgebras, can be solved. With certain properties of the positive root vectors, we obtain that the sufficient conditions of these modules are irreducibleL-modules, whereL=W(0∣n),S(0∣n), andK(n).

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de VEGA, H. J., and V. A. FATEEV. "FACTORIZABLE S MATRICES FOR PERTURBED W-INVARIANT THEORIES." International Journal of Modern Physics A 06, no. 18 (July 30, 1991): 3221–34. http://dx.doi.org/10.1142/s0217751x91001568.

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[Formula: see text]-invariant conformal field theories admit perturbations preserving integrability and leading to massive quantum field theories. The unitary and crossing-invariant S matrices of such QFTs are explicitly constructed by restricting the SL (n, q)-symmetric solutions of the Yang-Baxter equations when qn+k=1. These scattering theories possess level-rank duality (n↔k).

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Tomina, N. N., P. C. Solmanov, N. M. Maksimov, and A. A. Pimerzin. "Hydrotreatment of petroluem on Ni6-PMo n W(12–n)(S)/Al2O3 catalysts." Catalysis in Industry 7, no. 4 (October 2015): 307–13. http://dx.doi.org/10.1134/s2070050415040157.

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Alrowaili, Dalal, Zohaib Zahid, Muhammad Ahsan, Sohail Zafar, and Imran Siddique. "Edge Metric Dimension of Some Classes of Toeplitz Networks." Journal of Mathematics 2021 (December 17, 2021): 1–11. http://dx.doi.org/10.1155/2021/3402275.

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Toeplitz networks are used as interconnection networks due to their smaller diameter, symmetry, simpler routing, high connectivity, and reliability. The edge metric dimension of a network is recently introduced, and its applications can be seen in several areas including robot navigation, intelligent systems, network designing, and image processing. For a vertex s and an edge g = s 1 s 2 of a connected graph G , the minimum number from distances of s with s 1 and s 2 is called the distance between s and g . If for every two distinct edges s 1 , s 2 ∈ E G , there always exists w 1 ɛ W E ⊆ V G , such that d s 1 , w 1 ≠ d s 2 , w 1 ; then, W E is named as an edge metric generator. The minimum number of vertices in W E is known as the edge metric dimension of G . In this study, we consider four families of Toeplitz networks T n 1,2 , T n 1,3 , T n 1,4 , and T n 1,2,3 and studied their edge metric dimension. We prove that for all n ≥ 4 , e dim T n 1,2 = 4 , for n ≥ 5 , e dim T n 1,3 = 3 , and for n ≥ 6 , e dim T n 1,4 = 3 . We further prove that for all n ≥ 5 , e dim T n 1,2,3 ≤ 6 , and hence, it is bounded.

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Khemira, Habib, P. B. Lombard, David Sugar, and Anita N. Azarenko. "Hedgerow Orientation Affects Canopy Exposure, Flowering, and Fruiting of `Anjou' Pear Trees." HortScience 28, no. 10 (October 1993): 984–87. http://dx.doi.org/10.21273/hortsci.28.10.984.

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Mature hedgerows of `Anjou' pear (Pyrus communis L.) trees, planted north(N)-south (S) or east (E)-west (W), were used to study the effect of hedgerow orientation on fruiting and canopy exposure. In 1990, flower bud density tended to be lower on the E-W rows, especially on their N sides. Fruit set (FS) was highest on the S side of E-W rows and lowest on the N side, while the E and W sides of the N-S rows were intermediate. Crop density (CD) had a similar pattern as FS, with more fruit on the S than on the N side of the E-W rows. CD was more evenly distributed between the sides on the N-S hedgerows. Differences in FS and CD between sides were related to different levels of sunlight interception. Light exposure was lowest on the N sides of the E-W rows and highest on the S sides throughout the growing season and especially toward the equinoxes. Increased exposure to the sun on the S and W sides late in the season led to more fruit with solar injury. Fruit from E–W rows were larger and less firm. Accumulated yields over 11 years showed a 21.4% increase in the N-S rows over those of the E-W rows.

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HO, JEFFREY D., MARK LINDQUIST, LAURA BULTMAN, and CHAD TORSTENSON. "A PATHY I S N OT W ELCOME H ERE." Prehospital Emergency Care 7, no. 3 (January 2003): 414–16. http://dx.doi.org/10.1080/10903120390936734.

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Nossa, A., and A. Cavaleiro. "Chemical and physical characterization of C(N)-doped W–S sputtered films." Journal of Materials Research 19, no. 8 (August 2004): 2356–65. http://dx.doi.org/10.1557/jmr.2004.0293.

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The load-bearing capacity of self-lubricating W–S films can be improved by doping with nitrogen or carbon. In this study, the chemical composition, the atomic bonding, the structure, and the surface and cross section morphologies of sputtered W–S–C(N) films were analyzed. The addition of the doping element leads to a progressive broadening of the x-ray diffraction (XRD) peaks indicating a loss of crystallinity. In W–S–N films, amorphous structure could be obtained. In W–S–C films, W–C compounds were detected in conjunction with the hexagonal WS2 phase. For the highest C contents, a nanocomposite structure, including those phases and graphite, was suggested for the film. X-ray photoelectron spectroscopy results showed different types of bonds in the W4f peak in good agreement with the XRD results, i.e., when W–C(N) compounds were indexed W–S, W–C, and W–N bonds are present in the W4f peak. For the highest C content film, the detection of C–C bond in the C1s peak confirmed the formation of graphite.

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Maghfirah, Ardhian, Haripamyu ., and Efendi . "KARAKTERISTIK PERMUKAAN REGULAR DI R n." Jurnal Matematika UNAND 7, no. 3 (February 19, 2019): 9. http://dx.doi.org/10.25077/jmu.7.3.9-15.2018.

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Secara umum, permukaan dapat dikatakan sebagai bagian dari R3 , dimana untuk setiap titik p di suatu lingkungan tertentu di R3 yang dimisalkan dengan S, terdapat suatu himpunan buka di R2 yang dimisalkan dengan U dan suatu himpunan buka di R3 yang dimisalkan dengan W yang memuat p sedemikian sehingga S ∩W homeomorfik pada U. Selanjutnya, suatu permukaan disebut sebagai permukaan regular apabila terdapat suatu pemetaan x dari U ∈ R2 ke S ∩ W ∈ R3 yang terdiferensial dan pemetaan tersebut memiliki turunan (dx) yang satu-satu untuk setiap titik di U. Untuk lebih memahami apa itu permukaan regular, pada makalah ini akan dijelaskan definisi dari permukaan regular dan apa saja karakteristik dari permukaan regular tersebut khususnya karakteristik dari suatu permukaan regular di R3 .Kata Kunci: Lingkungan, terdiferensial, himpunan buka, pemetaan, homeomorfik, permukaan, permukaan regular

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Robert, Frédéric. "Nondegeneracy of positive solutions to nonlinear Hardy–Sobolev equations." Advances in Nonlinear Analysis 6, no. 2 (May 1, 2017): 237–42. http://dx.doi.org/10.1515/anona-2016-0267.

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AbstractIn this note, we prove that the kernel of the linearized equation around a positive energy solution in ${\mathbb{R}^{n}}$, ${n\geq 3}$, to the problem $-\Delta W-\gamma|x|^{-2}V=|x|^{-s}W^{2^{\star}(s)-1}$ is one-dimensional when $s+\gamma>0$. Here, ${s\in[0,2)}$, ${0\leq\gamma<(n-2)^{2}/4}$ and ${2^{\star}(s)=2(n-s)/(n-2)}$.

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BUFFON, L. O., A. ZADRA, and D. DALMAZI. "CLASSICAL AND QUANTUM N=1 SUPER W∞-ALGEBRAS." Modern Physics Letters A 11, no. 29 (September 21, 1996): 2339–49. http://dx.doi.org/10.1142/s0217732396002332.

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We construct higher-spin N=1 superalgebras as extensions of the super-Virasoro algebra containing generators for all spins s≥3/2. We find two distinct classical (Poisson) algebras on the phase superspace. Our results indicate that only one of them can be consistently quantized.

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Linshaw, Andrew R. "Universal two-parameter 𝒲∞-algebra and vertex algebras of type 𝒲(2, 3, …, N)." Compositio Mathematica 157, no. 1 (January 2021): 12–82. http://dx.doi.org/10.1112/s0010437x20007514.

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We prove the longstanding physics conjecture that there exists a unique two-parameter ${\mathcal {W}}_{\infty }$-algebra which is freely generated of type ${\mathcal {W}}(2,3,\ldots )$, and generated by the weights $2$ and $3$ fields. Subject to some mild constraints, all vertex algebras of type ${\mathcal {W}}(2,3,\ldots , N)$ for some $N$ can be obtained as quotients of this universal algebra. As an application, we show that for $n\geq 3$, the structure constants for the principal ${\mathcal {W}}$-algebras ${\mathcal {W}}^k({\mathfrak s}{\mathfrak l}_n, f_{\text {prin}})$ are rational functions of $k$ and $n$, and we classify all coincidences among the simple quotients ${\mathcal {W}}_k({\mathfrak s}{\mathfrak l}_n, f_{\text {prin}})$ for $n\geq 2$. We also obtain many new coincidences between ${\mathcal {W}}_k({\mathfrak s}{\mathfrak l}_n, f_{\text {prin}})$ and other vertex algebras of type ${\mathcal {W}}(2,3,\ldots , N)$ which arise as cosets of affine vertex algebras or nonprincipal ${\mathcal {W}}$-algebras.

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García-García, J. I., D. Marín-Aragón, and A. Vigneron-Tenorio. "Union of Sets of Lengths of Numerical Semigroups." Mathematics 8, no. 10 (October 15, 2020): 1789. http://dx.doi.org/10.3390/math8101789.

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Let S=⟨a1,…,ap⟩ be a numerical semigroup, let s∈S and let Z(s) be its set of factorizations. The set of lengths is denoted by L(s)={L(x1,⋯,xp)∣(x1,⋯,xp)∈Z(s)}, where L(x1,⋯,xp)=x1+⋯+xp. The following sets can then be defined: W(n)={s∈S∣∃x∈Z(s)suchthatL(x)=n}, ν(n)=⋃s∈W(n)L(s)={l1<l2<⋯<lr} and Δν(n)={l2−l1,…,lr−lr−1}. In this paper, we prove that the function Δν:N→P(N) is almost periodic with period lcm(a1,ap).

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Bakery, Awad A., and M. H. El Dewaik. "A Generalization of Caristi’s Fixed Point Theorem in the Variable Exponent Weighted Formal Power Series Space." Journal of Function Spaces 2021 (June 5, 2021): 1–18. http://dx.doi.org/10.1155/2021/9919420.

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Suppose p n be sequence of positive reals. By H w p n , we represent the space of all formal power series ∑ n = 0 ∞ a n z n equipped with ∑ n = 0 ∞ λ a n / n + 1 p n < ∞ , for some λ > 0 . Various topological and geometric behavior of H w p n and the prequasi ideal constructs by s -numbers and H w p n have been considered. The upper bounds for s -numbers of infinite series of the weighted n -th power forward shift operator on H w p n with applications to some entire functions are granted. Moreover, we investigate an extrapolation of Caristi’s fixed point theorem in H w p n .

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Erwin, Terry L. "ARBOREAL BEETLES OF TROPICAL FORESTS: THE XYSTOSOMI GROUP, SUBTRIBE XYSTOSOMINA (COLEOPTERA: CARABIDAE: BEMBIDIINI). PART I. CHARACTER ANALYSIS, TAXONOMY, AND DISTRIBUTION." Canadian Entomologist 126, no. 3 (June 1994): 549–666. http://dx.doi.org/10.4039/ent126549-3.

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AbstractA group of subarboreal tropical beetles, the Xystosomi of subtribe Xystosomina new subtribe, is revised and reclassified based on a reevaluation of structural characters. Xystosomi are found in tropical Australia (Queensland) and tropical/subtropical America (Guerrero, México, to Aguas Blancas, Argentina). The largest concentration of species occurs near the equator in the Amazon Basin, but a significant radiation of flightless forms was recently discovered in the northern Andes of Colombia, Ecuador, and Venezuela. Xystosomina also includes the Mioptachyi, which at present is composed of the genera Mioptachys and Inpa.Seventy-six species of Neotropical and Australian Xystosomi are described or re-described, illustrated, or keyed. This assemblage includes 12 classic species, 24 species described in the last 3 decades, and 40 new species, a 6-fold increase since the time of Henry Walter Bates, the last 19th-century entomologist to study this remarkable lineage of carabid beetles. The Xystosomi are now arrayed in five genera: Philipis gen.nov. (type: Tachys trunci Darlington, Australia), Geballusa gen.nov. (type: Xystosomus microtretus Erwin, Costa Rica), Gouleta gen.nov. (type: Bembidion cayennense Dejean, Brazil), Batesiana gen.nov. (type: Xystosomus gruti Bates, Brazil), and Xystosomus Schaum (type: Xystosomus inflatus Schaum, Brazil).The following specific taxa are described as new (type-locality in parentheses): Geballusa rex (Brazil: 06°02′N 050°17′W), oligotreta (Panamá: 08°40′N 079°56′W), nannotreta (Brazil: 02°54′S 059°57′W), Gouleta gentryi (Perú: 12°50′S 069°20′W), Batesiana para (Brazil: 01°22′S 048°20′W), angustia (Perú: 05°08′S 074°45′W), samiria (Perú: 05°08′S 074°45′W), esheje (Perú: 05°08′S 074°45′W), crassa (Perú: 03°15′S 072°55′W), notesheje (Perú: 03°15′S 072°55′W), manusculptilis (Perú: 12°07′S 070°58′W), parapara (Brazil: 02°28′S 046°26′W), am (Perú: 05°08′S 074°45′W), indetecticostis (Ecuador: 00°57′S 077°48′W), nox (Ecuador: 00°57′S 077°48′W), parkeri (Perú: 03°15′S 072°55′W), hamatilis (Ecuador: 01°02′S 077°40′W), notparkeri (Colombia: 00°08′N 075°51′W), pfunorum (Perú: 03°15′S 072°55′W), quadrata (Perú: 03°15′S 072°55′W), protosculptilis (Perú: 12°50′S 069°20′W), misahualli (Ecuador: 01°02′S 077°40′W), depressisculptilis (Ecuador: 01°02′S 077°40′W), irisculptilis (Ecuador: 00°24′S 076°37′W), foveosculptilis (Brazil: 02°28′S 046°26′W), punctisculptilis (Perú: 03°15′S 072°55′W), eugeneae (Perú: 11°56′47″S 071°17′00″W), anchicaya (Colombia: 03°43′N 076°57′W), jefe (Panamá: 09°12′N 079°21′W), exigupunctata (Perú: 05°08′S 074°45′W), rosebudae (Ecuador: 00°57′S 077°48′W), equanegrei (Ecuador: 00°57′S 077°48′W), henryi (Ecuador: 00°28′S 077°53′W), baeza (Ecuador: 00°57′S 077°48′W), huacamayas (Ecuador: 00°28′S 077°53′W), dannyi (Ecuador: 00°57′S 077°48′W), alticola (Colombia: 04°21′S 074°22′W), jacupiranga (Brazil: 24°42′S 048°00′W), chiriboga (Ecuador: 00°15′S 078°44′W), wygo (Colombia: 04°53′N 074°31′W).The following names are resurrected from synonymy for good species: hilaris Bates and belti Bates. Several name combinations were changed as a result of the generic reorganization: Philipis trunci (Darlington), Geballusa microtreta (Erwin), G. polytreta (Erwin), Gouleta notiophiloides (Erwin), G. spangleri (Erwin), G. cayennense (Dejean), Batesiana bisulcifrons (Erwin), B. negrei (Erwin), B. hilaris (Bates), B. belti (Bates), B. ampliata (Bates), B. strigosa (Bates), B. gruti (Bates), B. nigripalpis (Erwin), B. villiersi (Perrault), B. apicisulcata (Erwin), B. iris (Erwin), B. sculpticollis (Bates), B. sulcicostis (Bates), B. anterocostis (Erwin), B. ovatula (Bates), B. grossipunctata (Erwin), B. batesi (Erwin), B. seriata (Erwin), B. sublaevis (Bates), B. aetholia (Erwin), B. parainsularis (Erwin), NEW COMBINATIONS.Results of the Xystosomi character analysis provided impetus for a reanalysis of the classification of the major lineages of the more inclusive group, Bembidiini, to discover where the Xystosomi might belong and, in turn, if our understanding of the Bembidiini itself needed adjustment. These results are implied in Part I, but presented in detail in a separate paper, Part II. Phylogeny and Zoogeography, along with supplemental taxonomic information.

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Dufault, Robert J., Benigno Villalon, and Mark Q. Smith. "Orientation of Root and Cotyledon in Pepper Seedlings and Its Use in Field Production." HortScience 22, no. 3 (June 1987): 418–20. http://dx.doi.org/10.21273/hortsci.22.3.418.

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Abstract ‘TAMBel-2’ bell pepper transplants (Capsicum annuum L.) were grown in a greenhouse for 39 days in north–south (N–S) oriented trays. About 69% of the plants had monodirectional (one plane pointing either N–S, E–W, NW–SE, or SW–NE) lateral root patterns, 23% had bidirectional (two planes), and 7% had omnidirectional (all around) root patterns relative to a N–S greenhouse tray orientation. Transplants were planted with cotyledons N–S (parallel to the N–S bed), with cotyledons E–W (perpendicular to the N–S bed), and at random, without regard to orientation. These plants subsequently were cultivated either deeply (9 cm) or shallowly (3 cm) 3, 5, and 7 weeks after transplanting. Transplants planted E–W by cotyledon orientation yielded significantly more early and overall marketable pods in contrast to those planted N–S by cotyledon orientation or at random. Deep cultivation decreased productivity in contrast to shallow cultivation and negated any benefit to E–W cotyledon orientation. Root and cotyledon orientations in field-seeded peppers were determined for ‘Hidalgo’, ‘TAM-Mild Chile-2’, ‘TAMBel-2’, and ‘Grand Rio 66’ peppers ≈2 months after field-seeding. At least 95% of the populations in all cultivars had monodirectional root orientations. Generally, orientations were divided equally among N–S, E–W, NW–SE, and NE–SW directions. Cotyledon orientation highly correlated with root orientation in all cultivars.

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32

Jarohs, Sven. "Strong Comparison Principle for the Fractional p-Laplacian and Applications to Starshaped Rings." Advanced Nonlinear Studies 18, no. 4 (November 1, 2018): 691–704. http://dx.doi.org/10.1515/ans-2017-6039.

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AbstractIn the following, we show the strong comparison principle for the fractional p-Laplacian, i.e. we analyze\quad\left\{\begin{aligned} \displaystyle(-\Delta)^{s}_{p}v+q(x)\lvert v\rvert% ^{p-2}v&\displaystyle\geq 0&&\displaystyle\phantom{}\text{in ${D}$},\\ \displaystyle(-\Delta)^{s}_{p}w+q(x)\lvert w\rvert^{p-2}w&\displaystyle\leq 0&% &\displaystyle\phantom{}\text{in ${D}$},\\ \displaystyle v&\displaystyle\geq w&&\displaystyle\phantom{}\text{in ${\mathbb% {R}^{N}}$},\end{aligned}\right.where {s\in(0,1)}, {p>1}, {D\subset\mathbb{R}^{N}} is an open set, and {q\in L^{\infty}(\mathbb{R}^{N})} is a nonnegative function. Under suitable conditions on s, p and some regularity assumptions on v, w, we show that either {v\equiv w} in {\mathbb{R}^{N}} or {v>w} in D. Moreover, we apply this result to analyze the geometry of nonnegative solutions in starshaped rings and in the half space.

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33

Campagnolo, Marcelo, Ricardo Reis, Marcele Santos, Lúcia Kliemann, and Ricardo Savaris. "Which mode and potency of electrocoagulation yields the Smallest Unobstructed Area of the Fallopian Tubes?" Revista Brasileira de Ginecologia e Obstetrícia / RBGO Gynecology and Obstetrics 40, no. 06 (May 29, 2018): 332–37. http://dx.doi.org/10.1055/s-0038-1656718.

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Objective To determine which mode and potency of electrocoagulation, using a modern electrosurgical generator, yields the smallest unobstructed area of the Fallopian tubes. Methods In an experimental study, tubes from 48 hysterectomies or tubal ligation were evaluated. Tubes were randomly allocated to one of the following groups: group A) 25 W x 5 seconds (n = 17); group B) 30 W x 5 seconds (n = 17); group C) 35 W x 5 seconds (n = 18), group D) 40 W x 5 seconds (n = 20); group E) 40 W x 5 seconds with visual inspection (blanch, swells, collapse) (n = 16); group F) 50 W x 5 seconds (n = 8). Bipolar electrocoagulation was performed in groups A to E, and monopolar electrocoagulation was performed in group F. Coagulation mode was used in all groups. Digital photomicrography of the transversal histological sections of the isthmic segment of the Fallopian tube were taken, and the median percentage of unobstructed luminal area (mm2) was measured with ImageJ software (ImageJ, National Institutes of Health, Bethesda, MD, USA). The Kruskal-Wallis test or analysis of variance (ANOVA) was used for statistical analysis. Results Ninety-six Fallopian tube sections were analyzed. The smallest median occluded area (%; range) of the Fallopian tube was obtained in the group with 40 W with visual inspection (8.3%; 0.9–40%), followed by the groups 25 W (9.1%; 0–35.9%), 40 W (14.2; 0.9–43.2%), 30 W (14.2; 0.9–49.7%), 35 W (15.1; 3–46.4%) and 50 W (38.2; 3.1–51%). No statistically significant difference was found among groups (p = 0.09, Kruskal-Wallis test). Conclusion The smallest unobstructed area was obtained with power setting at 40 W with visual inspection using a modern electrosurgical generator. However, no statistically significant difference in the unobstructed area was observed among the groups using these different modes and potencies.

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34

Xu, Shun. "An Equivalent Condition and Some Properties of Strong J-Symmetric Ring." Journal of Mathematics 2021 (September 22, 2021): 1–6. http://dx.doi.org/10.1155/2021/7335202.

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Let J R denote the Jacobson radical of a ring R . We say that ring R is strong J-symmetric if, for any a , b , c ∈ R , a b c ∈ J R implies b a c ∈ J R . If ring R is strong J-symmetric, then it is proved that R x / x n is strong J-symmetric for any n ≥ 2 . If R and S are rings and W S R is a R , S -bimodule, E = T R , S , W = R W 0 S = r w 0 s | r ∈ R , w ∈ W , s ∈ S , then it is proved that R and S are J-symmetric if and only if E is J-symmetric. It is also proved that R and S are strong J-symmetric if and only if E is strong J-symmetric.

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Sanquetta, Carlos Roberto, Thiago Wendling Gonçalves de Oliveira, Ana Paula Dalla Corte, Mateus Niroh Inoue Sanquetta, and Greyce Charllyne Benedet Maas. "ANÁLISE DA PRODUÇÃO, IMPORTAÇÃO, EXPORTAÇÃO E CONSUMO APARENTE DE PAPEL NO BRASIL ENTRE 1961 E 2016." BIOFIX Scientific Journal 4, no. 2 (March 30, 2019): 110. http://dx.doi.org/10.5380/biofix.v4i2.64881.

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O segmento de papel e celulose tem posição de destaque na economia do setor florestal brasileiro e mundial. O objetivo deste estudo foi analisar a dinâmica da produção, importação, exportação e consumo aparente de três tipos de papéis (P+W: imprimir e escrever, H+S: uso doméstico e sanitário e N: jornal) no período de 1961 a 2016. Para essa análise foram utilizados dados extraídos do sistema FAOSTAT da FAO. Os resultados encontrados demonstram que nesse período foram produzidas 77 M t de P+W, 24 M t de H+S e 9 M t de N. As importações totalizaram 10 M t, 188 mil t e 12 M t, respectivamente para P+W, H+S e N. As exportações no período foram de 25 M t, 500 mil t e 334 mil t, respectivamente. O consumo aparente foi de 61 M t, 24 M t e 21 M t, respectivamente. O consumo médio per capita desses papéis no período foi de 6,98; 2,58 e 2,57 kg.hab-1. O consumo de H+S deu-se de forma crescente em toda a série temporal, enquanto que para P+W e N foi decrescente, sobretudo a partir de 2010. O Brasil é superavitário em P+W e H+S e deficitário na balança comercial em N. Conclui-se que há uma tendência de queda de consumo em P+W e N e aumento de H+S, essa tendência é verificada na produção, importação e consumo. As exportações de H+S e N ainda são pouco expressivas. Já as importações de P+W e N apresentaram tendência de queda desde 2010.

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Водопьянов, Сергей Константинович, Sergei Konstantinovich Vodopyanov, Александр Иванович Тюленев, and Alexander Ivanovich Tyulenev. "Пространства Соболева $W^{1}_{p}$ на $d$-толстых замкнутых подмножествах $\mathbb{R}^{n}$." Математический сборник 211, no. 6 (May 25, 2020): 40–94. http://dx.doi.org/10.4213/sm9199.

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Пусть $S \subset \mathbb{R}^{n}$ - замкнутое непустое множество такое, что для некоторых $d \in [0,n]$ и $\varepsilon>0$ $d$-вместимость по Хаусдорфу $\mathscr{H}^{d}_{\infty}(S \cap Q(x,r)) \geq \varepsilon r^{d}$ для всех кубов $Q(x,r)$ с центрами в $x \in S$ и длинами ребер $2r \in (0,2]$. Для каждого $p>\max\{1,n-d\}$ мы даем внутреннюю характеризацию пространства следов $W_{p}^{1}(\mathbb{R}^{n})|_{S}$ на множестве $S$ пространства Соболева $W_{p}^{1}(\mathbb{R}^{n})$. Более того, мы доказываем существование ограниченного линейного оператора продолжения $\operatorname{Ext}\colon W_{p}^{1}(\mathbb{R}^{n})|_{S} \to W_{p}^{1}(\mathbb{R}^{n})$, являющегося правым обратным для стандартного оператора следа. Тем самым мы обобщаем соответственно те результаты, которые были получены ранее в случае $p \in (1,n]$ для регулярных по Альфорсу множеств $S$. Библиография: 36 названий.

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37

Shumyatsky, Pavel, and Danilo Silveira. "On finite groups in which commutators are covered by Engel subgroups." Journal of Group Theory 22, no. 6 (November 1, 2019): 1049–57. http://dx.doi.org/10.1515/jgth-2019-0002.

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Abstract Let {m,n} be positive integers and w a multilinear commutator word. Assume that G is a finite group having subgroups {G_{1},\ldots,G_{m}} whose union contains all w-values in G. Assume further that all elements of the subgroups {G_{1},\ldots,G_{m}} are n-Engel in G. It is shown that the verbal subgroup {w(G)} is s-Engel for some {\{m,n,w\}} -bounded number s.

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38

Vieira, Antonio José Dias, Dario Alves de Oliveira, Taís Cristina Bastos Soares, Ivan Schuster, Newton Deniz Piovesan, Carlos Alberto Martínez, Everaldo Gonçalves de Barros, and Maurílio Alves Moreira. "Use of the QTL approach to the study of soybean trait relationships in two populations of recombinant inbred lines at the F7 and F8 generations." Brazilian Journal of Plant Physiology 18, no. 2 (June 2006): 281–90. http://dx.doi.org/10.1590/s1677-04202006000200004.

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This work aimed to identify the quantitative trait loci (QTL) associated with photosynthesis and growth and productivity traits of soybean and to study possible associations between these traits by the analysis of coincidence of QTL in linkage groups (LGs). Thus, populations of recombinant inbred lines (RILs) of the F7 and F8 generations derived from the cross between the varieties BARC-8 and Garimpo were used. The traits evaluated were net assimilation rate of CO2 under saturating light (Asat), potential photosynthesis rate (Pmax), leaf area (A), specific leaf area (SLA), specific leaf nitrogen (N); root (W R), nodule (W N), stem (W ST), leaf (W L), pod (W P) and plant dry mass (W T); nodule (nN), seed (n s), and pod number (nP); seed fresh mass per plant (W S), one-hundred seed fresh mass (W HS) and seed protein percentage (P%). It was possible to identify the following QTL associated with the following soybean traits: SLA, Asat, N, W R, W ST, W L, W T, W P, W HS, n s and nP, indicating that the RIL population has a great potential for mapping loci associated with quantitative traits of the soybean crop. The correlations between the soybean traits were partially confirmed by coincidence of QTL.

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39

Huang, Haiyan. "Error bounds on multivariate Normal approximations for word count statistics." Advances in Applied Probability 34, no. 03 (September 2002): 559–86. http://dx.doi.org/10.1017/s0001867800011769.

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Given a sequence S and a collection Ω of d words, it is of interest in many applications to characterize the multivariate distribution of the vector of counts U = (N(S,w 1), …, N(S,w d )), where N(S,w) is the number of times a word w ∈ Ω appears in the sequence S. We obtain an explicit bound on the error made when approximating the multivariate distribution of U by the normal distribution, when the underlying sequence is i.i.d. or first-order stationary Markov over a finite alphabet. When the limiting covariance matrix of U is nonsingular, the error bounds decay at rate O ((log n) / √n) in the i.i.d. case and O ((log n)3 / √n) in the Markov case. In order for U to have a nondegenerate covariance matrix, it is necessary and sufficient that the counted word set Ω is not full, that is, that Ω is not the collection of all possible words of some length k over the given finite alphabet. To supply the bounds on the error, we use a version of Stein's method.

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40

Zhang, Caifeng. "Trudinger–Moser Inequalities in Fractional Sobolev–Slobodeckij Spaces and Multiplicity of Weak Solutions to the Fractional-Laplacian Equation." Advanced Nonlinear Studies 19, no. 1 (February 1, 2019): 197–217. http://dx.doi.org/10.1515/ans-2018-2026.

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Abstract In line with the Trudinger–Moser inequality in the fractional Sobolev–Slobodeckij space due to [S. Iula, A note on the Moser–Trudinger inequality in Sobolev–Slobodeckij spaces in dimension one, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 28 2017, 4, 871–884] and [E. Parini and B. Ruf, On the Moser–Trudinger inequality in fractional Sobolev–Slobodeckij spaces, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 29 2018, 2, 315–319], we establish a new version of the Trudinger–Moser inequality in {W^{s,p}(\mathbb{R}^{N})} . Define \lVert u\rVert_{1,\tau}=\bigl{(}[u]^{p}_{W^{s,p}(\mathbb{R}^{N})}+\tau\lVert u% \rVert_{p}^{p}\bigr{)}^{\frac{1}{p}}\quad\text{for any }\tau>0. There holds \sup_{u\in W^{s,p}(\mathbb{R}^{N}),\lVert u\rVert_{1,\tau}\leq 1}\int_{\mathbb% {R}^{N}}\Phi_{N,s}\bigl{(}\alpha\lvert u\rvert^{\frac{N}{N-s}}\bigr{)}<+\infty, where {s\in(0,1)} , {sp=N} , {\alpha\in[0,\alpha_{*})} and \Phi_{N,s}(t)=e^{t}-\sum_{i=0}^{j_{p}-2}\frac{t^{j}}{j!}. Applying this result, we establish sufficient conditions for the existence of weak solutions to the following quasilinear nonhomogeneous fractional-Laplacian equation: (-\Delta)_{p}^{s}u(x)+V(x)\lvert u(x)\rvert^{p-2}u(x)=f(x,u)+\varepsilon h(x)% \quad\text{in }\mathbb{R}^{N}, where {V(x)} has a positive lower bound, {f(x,t)} behaves like {e^{\alpha\lvert t\rvert^{N/(N-s)}}} , {h\in(W^{s,p}(\mathbb{R}^{N}))^{*}} and {\varepsilon>0} . Moreover, we also derive a weak solution with negative energy.

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Dharmarha, Preeti, and Sonu Ram. "Spectral mapping theorem and Weyl’s theorem for (m,n)-paranormal operators." Filomat 35, no. 10 (2021): 3293–302. http://dx.doi.org/10.2298/fil2110293d.

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In the present paper, we prove spectral mapping theorem for (m,n)-paranormal operator T on a separable Hilbert space, that is, f (?w(T)) = ?w(f(T)) when f is an analytic function on some open neighborhood of ?(T). We also show that for (m,n)-paranormal operator T, Weyl?s theorem holds, that is, ?(T)-?w(T) = ?00(T). Moreover, if T is algebraically (m,n)-paranormal, then spectral mapping theorem and Weyl?s theorem hold.

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42

Ramm, Alexander G. "When does a double-layer potential equal to a single-layer one?" AIMS Mathematics 7, no. 10 (2022): 19287–91. http://dx.doi.org/10.3934/math.20221058.

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<abstract>Let $ D $ be a bounded domain in $ {{\mathbb R}}^3 $ with a closed, smooth, connected boundary $ S $, $ N $ be the outer unit normal to $ S $, $ k > 0 $ be a constant, $ u_{N^{\pm}} $ are the limiting values of the normal derivative of $ u $ on $ S $ from $ D $, respectively $ D': = {{\mathbb R}}^3\setminus \bar{D} $; $ g(x, y) = \frac{e^{ik|x-y|}}{4\pi |x-y|} $, $ w: = w(x, \mu): = \int_S g_{N}(x, s)\mu(s)ds $ be the double-layer potential, $ u: = u(x, \sigma): = \int_S g(x, s)\sigma(s)ds $ be the single-layer potential. In this paper it is proved that for every $ w $ there is a unique $ u $, such that $ w = u $ in $ D $ and vice versa. This result is new, although the potential theory has more than 150 years of history. Necessary and sufficient conditions are given for the existence of $ u $ and the relation $ w = u $ in $ D' $, given $ w $ in $ D' $, and for the existence of $ w $ and the relation $ w = u $ in $ D' $, given $ u $ in $ D' $.</abstract>

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43

Pałka, Paweł. "Obowiązek rezydencji prałatów i kanoników katedralnej kapituły chełmskiej w Krasnymstawie." Prawo Kanoniczne 28, no. 3-4 (December 10, 1985): 223–36. http://dx.doi.org/10.21697/pk.1985.28.3-4.07.

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T h e q u e stio n show ed in a T itle of th is m o n o g rap h re g a rd th eC h a p te r c o n stitu te d in C hełm in v irtu e of F o u n d a tio n A ct of th eK in g W ład y sław Jag iełło fro m 1429, a n d tram sfered in 1490 to K ra sn y staw . F o r th e en d o v em e n t of thfe C h a p ter com posed in itia l fro m2 p re la te s a n d 10 canons d em an d e d th e K ing, th a t a ll m em b ers oft-he C h ap te r sh o u ld resid e by th e C a th e d ra l to k eep a sp len d o r ofG od’s C u lt a n d in o rd e r th a t th ey should say p re y e rs fo r th e fo u n d er,h is fam ily, th e deceased w ifes a n d fo r a p ro sp e rity of K ingdom .S im ila r resid en ce d em an d e d also T re n t’s C ouncil a n d C h a p te r’s C h a rte rs a p p ro v ed b y B ishop W ojciech Sobi-ejuski fro m S taro izrzeb iec in 1572. C ause a pooor endow m ent of th e C haiptar th e p ré la ts a n d th ecanons alm o st since a b eg in n in g assu m ed o th e r P a s to ra l’s b eneficesin a D iocese, it w as la ck of th e fu n d s a d e q u a te fo r all m em b ers ofa C h a p ter (in itial 12, a n d la te r 19) fo r su b sisten ce b esid e th e C ath e d ra l, chiefly th a t in som e y e ars th e e states of C h a p te r w e re dev a sta te d b y T a ta r’s invasions.G oing th ro u g h th e y ro u n d of d u ties th e B ishops w e re w a tc h in gab o u t th e fu lfilm e n t th e ir o b lig atio n of R esidence by p ré la ts an dcanons, a n d th ey w a tc h in g also th a t G od’s cu lt sh o u ld be rig h tlyp erfo rm ed , a t le a s t successively b y a p a rt of th e m em b ers of a C h ap te r. I t w as se ttle d a cu sto m co n cern in g th e p e rfo rm a n ce o f a C ulta n d th e fu lfilm e n t of d u ties re la te d to, in a fa rm of ro ta tio n design a te d by a C h ap ter.I t w e re w eek ly ro ta tio n , a n d o ften m o n th ly, com posed by tw o p ré la ts or canons. S om etim e o n ly th e y w e re re p la ce d b y h o n o ra ry canons. A lso th is m a n n e r of resid en ce w aist ev e ry tim e co n serv e v erye x actly , w h a t w as show ed in th e reco rd s of C h a p te r’s sessions a n din R e fo rm atio n al D ecrees issu ed b y B ishops a fte r th e acco m p lish m en ts of C a th e d ra l v isitatio n s.I t w as in a p rin c ip le d u rin g a ll tim e of th is C h a p te r ex istatio n ,w h ich w as ab ro g a te d to g e th e r w ith th e ab ro g a tio n o f C helm ’s diocese by a P o p e P iu s V II w ith a B u lla Q u em a d m o d u m R o m a n o ru mP o n tific u m fro m O ct. 9, 1805, p u t in to effect in 18C7, sim u ltan eo u slyto a c rea tio n of L u b lin ’s diocese a n d it C a th e d ra l C h ap ter.

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Marongiu, Sophia. ""Det blir ett totalt utanförskap" - könsperpektiv på kvinnors karriärutveckling." Tidskrift för genusvetenskap 17, no. 2 (June 20, 2022): 41–50. http://dx.doi.org/10.55870/tgv.v17i2.4735.

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T h e p u r p o s e of t h e p r o j e c t in this p a p e r is t o study w o m e n ' s c a r e e r d e v e l o p m e n t in o r d e r to e l u c i d a t e obstacles as well as a d v a n t a g e s f r o m a g e n d e r perspective. "Women in m a n a g e n t " s t u d i e s have so f a r mostly c o n c e n t r a t e d o n w o m e n already in a leadi n g p o s i t i o n . T h e p r o b l em is, however, that these women have very little t o say a b o u t why t h e numb e r of w o m e n in l e a d i n g p o s i t i o n is so small. For this reason I have concentrated on following the c a r e e r d e v e l o p m e n t of a g r o u p of w o m e n working o n lower levels of a big, d e c e n t r a l i s e d g o v e r m e n t a l o r g a n i s a t i o n . Some of t h e women have clear c a r e e r a m b i t i o n s ; they want to be p r o m o t e d and gain l e a d i n g positions, o t h e r s have not s t a t e d any personal i n t e r e s t in p u r s u i n g a career. T h e study conc e n t r a t e s on i n t e r a c t i o n a n d intrapsychological as well as s t r u c t u r a l m o d e l s of analysis a r e used. My h y p o t h e s i s is t h a t t h e c u l t u r a l r e p r e s e n t a t i o n s of f e m i n i n i t y a n d those of l e a d e r s h i p are diverg e n t , a fact w h i c h compels w o m e n to use specific s t r a t e g i e s in o r d e r to r e c o n c i l e g e n d e r identity with that of a leader. Since this article is a work-in-progess-report the r e u l t s I p r e s e n t a r e only p r e l i m i n a r y . It is possible, however, t o i d e n u f y at least two significant strategies. O n e c o u l d b e c a l l e d a g e n d e r - n e u t r a l strategy, wher e t h e s i g n i f i c a n c e of g e n d e r in l e a d e r s h i p is d e n i - e d a l t o g e t h e r . T h e o t h e r strategy is to emphasis e specific f e m a l e q u a l i t i e s as a tool to b e u s e d in ord e r t o c h a n g e t h e p r e v a i l i n g m a l e n o r m c o n n e c t e d with l e a d e r s h i p . T h e q u e s t i o n is w h e t h e r t h e organ i s a t i o n is p r e p a r e d to invest in t h o s e w o m e n who see themselves as p o t e n t i a l t r a n s f o r m e r s of tradit i o n a l male values. In a follow-up study I am g o i n g t o s c r u t i n i s e t h e s e l e c t i o n process in t h e oraganisat i o n in o r d e r to see which w o m e n are c h o s e n for l e a d i n g p o s i t i o n s in t h e f u t u r e .

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45

GRAHAM, COLIN C. "The support of pseudomeasures on." Mathematical Proceedings of the Cambridge Philosophical Society 142, no. 1 (January 2007): 149–52. http://dx.doi.org/10.1017/s0305004106009339.

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AbstractPM(E) denotes the set of pseudomeasures on $\mathbb{R}$ with support in the closed set E ⊆ $\mathbb{R}$. Then y ∈ $\mathbb{R}$ is not in E if and only if there is a neighbourhood W of y with $\lim_{N\to\infty} \int_{-N}^{N}(1-{|t|}/{N})e^{2\pi itw}\cal{F} S(t)\,dt=0$ uniformly for w ∈ W and S ∈ PM(E) with ‖S‖PM ≤ 1. This improves previous results by adding “uniformly” and its scope. The proof uses the fact that squashing the central spike of the Fejer kernel leads to A-norm convergence.

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Saniga, Metod, Henri de Boutray, Frédéric Holweck, and Alain Giorgetti. "Taxonomy of Polar Subspaces of Multi-Qubit Symplectic Polar Spaces of Small Rank." Mathematics 9, no. 18 (September 16, 2021): 2272. http://dx.doi.org/10.3390/math9182272.

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We study certain physically-relevant subgeometries of binary symplectic polar spaces W(2N−1,2) of small rank N, when the points of these spaces canonically encode N-qubit observables. Key characteristics of a subspace of such a space W(2N−1,2) are: the number of its negative lines, the distribution of types of observables, the character of the geometric hyperplane the subspace shares with the distinguished (non-singular) quadric of W(2N−1,2) and the structure of its Veldkamp space. In particular, we classify and count polar subspaces of W(2N−1,2) whose rank is N−1. W(3,2) features three negative lines of the same type and its W(1,2)’s are of five different types. W(5,2) is endowed with 90 negative lines of two types and its W(3,2)’s split into 13 types. A total of 279 out of 480 W(3,2)’s with three negative lines are composite, i.e., they all originate from the two-qubit W(3,2). Given a three-qubit W(3,2) and any of its geometric hyperplanes, there are three other W(3,2)’s possessing the same hyperplane. The same holds if a geometric hyperplane is replaced by a ‘planar’ tricentric triad. A hyperbolic quadric of W(5,2) is found to host particular sets of seven W(3,2)’s, each of them being uniquely tied to a Conwell heptad with respect to the quadric. There is also a particular type of W(3,2)’s, a representative of which features a point each line through which is negative. Finally, W(7,2) is found to possess 1908 negative lines of five types and its W(5,2)’s fall into as many as 29 types. A total of 1524 out of 1560 W(5,2)’s with 90 negative lines originate from the three-qubit W(5,2). Remarkably, the difference in the number of negative lines for any two distinct types of four-qubit W(5,2)’s is a multiple of four.

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47

Kwon, Oh Sang, Shahid Khan, Young Jae Sim, and Saqib Hussain. "Bounds for the Coefficient of Faber Polynomial of Meromorphic Starlike and Convex Functions." Symmetry 11, no. 11 (November 4, 2019): 1368. http://dx.doi.org/10.3390/sym11111368.

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Let Σ be the class of meromorphic functions f of the form f ( ζ ) = ζ + ∑ n = 0 ∞ a n ζ − n which are analytic in Δ : = { ζ ∈ C : | ζ | > 1 } . For n ∈ N 0 : = N ∪ { 0 } , the nth Faber polynomial Φ n ( w ) of f ∈ Σ is a monic polynomial of degree n that is generated by a function ζ f ′ ( ζ ) / ( f ( ζ ) − w ) . For given f ∈ Σ , by F n , i ( f ) , we denote the ith coefficient of Φ n ( w ) . For given 0 ≤ α < 1 and 0 < β ≤ 1 , let us consider domains H α and S β ⊂ C defined by H α = { w ∈ C : Re ( w ) > α } and S β = { w ∈ C : | arg ( w ) | < β } , which are symmetric with respect to the real axis. A function f ∈ Σ is called meromorphic starlike of order α if ζ f ′ ( ζ ) / f ( ζ ) ∈ H α for all ζ ∈ Δ . Another function f ∈ Σ is called meromorphic strongly starlike of order β if ζ f ′ ( ζ ) / f ( ζ ) ∈ S β for all ζ ∈ Δ . In this paper we investigate the sharp bounds of F n , n − i ( f ) , n ∈ N 0 , i ∈ { 2 , 3 , 4 } , for meromorphic starlike functions of order α and meromorphic strongly starlike of order β . Similar estimates for meromorphic convex functions of order α ( 0 ≤ α < 1 ) and meromorphic strongly convex of order β ( 0 < β ≤ 1 ) are also discussed.

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48

Gapich, D. S., S. D. Fomin, and E. V. Shiryaeva. "Dy-namics of the movement of the elastically fixed working body of the cultivator machine-tractor aggregates." Traktory i sel hozmashiny 84, no. 10 (October 15, 2017): 28–32. http://dx.doi.org/10.17816/0321-4443-66331.

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Tillage machines that have in their design elastic links in the fastening -f w-rking organs, under certain conditions, can generate active undamped -scillati-ns -f w-rking b-dies due t- the peculiarity -f the cutting pr-cess -f the s-il layer, which all-ws t- reduce the -verall level -f f-rce l-ading and the dynamism -f the functi-ning -f the entire system. At the same time, the questi-n -f the effect -f vibrati-ns -f the w-rking -rgan -n the agr-technical indices -f the -perati-n -f machine-tract-r aggregates, in particular -n the deviati-n -f the pr-cessing depth fr-m the mean value, bec-mes t-pical. The mathematical m-del describing dynamics -f m-vement -f the elastically fixed w-rking b-dy -f the cultivat-r machine-tract-r aggregates, taking int- acc-unt the f-rce, elastic and dissipative characteristics -f the links -f the system is c-nsidered in the article. Dissipative pr-perties -f s-il in the w-rk are characterized by the c-efficient -f attenuati-n -f the s-il envir-nment. The rigidity -f the elastic element in the attachment -f the w-rking member was determined fr-m the c-nditi-n that the frequency -f the natural -scillati-ns -f the system and the frequency -f the disturbing f-rce be equal, which c-rresp-nds t- a res-nant m-de -f -perati-n. Calculati-n -f this mathematical m-del all-wed t- determine the r--t-mean-square deviati-n -f the treatment depth and c-mpare its value with the value -f the devel-ped techn-l-gical t-lerance f-r the change in the rigidity -f the elastic element in the fastening -f the w-rking member, as a result -f which the f-ll-wing c-nclusi-ns were made: the use -f the self--scillati-n m-de -f the w-rking -rgans can significantly influence -n the stability -f the w-rking b-dy in the vertical plane, especially this affects the s-ils with weak dissipative pr-perties, It can be assumed that significant amplitude -scillati-ns -f the w-rking element in the h-riz-ntal plane can lead t- an increased abrasi-n -f the s-il backgr-und by the w-rking -rgan and, as a c-nsequence, t- an increase in the number -f er-ding particles in the s-il and the devel-pment -f wind er-si-n.

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49

Gómez-del-Campo, María, Ana Centeno, and David J. Connor. "Yield determination in olive hedgerow orchards. I. Yield and profiles of yield components in north - south and east - west oriented hedgerows." Crop and Pasture Science 60, no. 5 (2009): 434. http://dx.doi.org/10.1071/cp08252.

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A study of the vertical distribution of flowering and fruit set and of components of yield (fruit numbers, fruit size, and fruit oil content) was maintained for 2 years in N–S- and E–W-oriented olive hedgerows of comparable structure (row spacing 4 m, hedgerow height to 2.5 m, width c. 1 m) near Toledo, Spain (39.9°N). Mean yield of the N–S orchard was 1854 kg oil/ha without difference between sides or years. Yield of the E–W orchard was greater in 2006, producing 2290 kg/ha, but only 1840 kg/ha in 2007, the same as the N–S orchard. The S side of the E–W orchard yielded more (59%) than the N side in 2007. In both orchards and years, most fruit was produced at 1.0–2.0 m height and fruit density was the most influential component in these differences, reflecting more intense bud initiation in these upper layers. Other components that determined fruit number, fertile inflorescences, fruits per fertile inflorescence, and fruit drop were not significantly different between layers. Fruit characteristics depended on hedgerow position. In both N–S and E–W hedgerows, fruit high in the hedgerow was the largest, most mature, and with highest oil content. These differences were more marked in N–S than in E–W hedgerows. Fruit growth and development were concentrated from the middle of September until the end November. Oil content per fruit increased linearly during that period when 65% of final oil content was accumulated. Similar patterns were observed between sides. The results of yield and yield profiles are discussed in the general context of light interception. The results suggest the importance of hedgerow porosity, and distinct penetration patterns of direct-beam radiation through N–S and E–W hedgerows, as the basis for explanation of the high yield of the N side of E–W hedgerows.

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50

Mamedov, Farman, and Sara Monsurrò. "Sobolev inequality with non-uniformly degenerating gradient." Electronic Journal of Qualitative Theory of Differential Equations, no. 24 (2022): 1–19. http://dx.doi.org/10.14232/ejqtde.2022.1.24.

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In this paper we prove the following weighted Sobolev inequality in a bounded domain Ω ⊂ R n , n ≥ 1 , of a homogeneous space ( R n , ρ , w d x ) , under suitable compatibility conditions on the positive weight functions ( v , w , ω 1 , ω 2 , … , ω n ) and on the quasi-metric ρ , ( ∫ Ω | f | q v w d z ) 1 q ≤ C ∑ i = 1 N ( ∫ Ω | f z i | p ω i M S w d z ) 1 p , f ∈ L i p 0 ( Ω ¯ ) , where q ≥ p > 1 and M S denotes the strong maximal operator. Some corollaries on non-uniformly degenerating gradient inequalities are derived.

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Journal articles on the topic 'Hawkesbury (N.S.W.)'

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