Journal articles: 'U.R.S.S.) Constitution'

1

Brement, Marshall. "U. S.-U. S. S. R.: Possibilities in Partnership." Foreign Policy, no. 84 (1991): 107. http://dx.doi.org/10.2307/1148785.

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Siddiqui, Mohd Asif, Veena Pande, and Mohammad Arif. "Production, Purification, and Characterization of Polygalacturonase from Rhizomucor pusillus Isolated from Decomposting Orange Peels." Enzyme Research 2012 (October 17, 2012): 1–8. http://dx.doi.org/10.1155/2012/138634.

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A thermophilic fungal strain producing polygalacturonase was isolated after primary screening of 40 different isolates. The fungus was identified as Rhizomucor pusilis by Microbial Type Culture Collection (MTCC), Chandigarh, India. An extracellular polygalacturonase (PGase) from R. pusilis was purified to homogeneity by two chromatographic steps using Sephadex G-200 and Sephacryl S-100. The purified enzyme was a monomer with a molecular weight of 32 kDa. The PGase was optimally active at 55°C and at pH 5.0. It was stable up to 50°C for 120 min of incubation and pH condition between 4.0 and 5.0. The stability of PGase decreases rapidly above 60°C and above pH 5.0. The apparent Km and Vmax values were 0.22 mg/mL and 4.34 U/mL, respectively. It was the first time that a polygalacturonase enzyme was purified in this species. It would be worthwhile to exploit this strain for polygalacturonase production. Polygalacturonase from this strain can be recommended for the commercial production because of its constitutive and less catabolically repressive nature, thermostability, wide range of pH, and lower Km properties. However, scale-up studies are needed for the better output for commercial production.

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Smyser, W. R. "U. S. S. R.-Germany: A Link Restored." Foreign Policy, no. 84 (1991): 125. http://dx.doi.org/10.2307/1148786.

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4

Henkin, Louis. "The Universal Declaration and the U. S. Constitution." PS: Political Science and Politics 31, no. 3 (September 1998): 512. http://dx.doi.org/10.2307/420609.

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5

Bramwell, Austin W. "Against Originalism: Getting over the U. S. constitution." Critical Review 16, no. 4 (January 2004): 431–53. http://dx.doi.org/10.1080/08913810408443618.

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Grace, Colin, and Elisabeth P. Nacheva. "Are CML Lymphoid Blast Crisis and Ph Positive ALL Genomically Indistinguishable?" Blood 116, no. 21 (November 19, 2010): 4464. http://dx.doi.org/10.1182/blood.v116.21.4464.4464.

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Abstract Abstract 4464 Philadelphia positive malignant disorders are a clinically divergent group of hemoblastoses with a unique identifying feature, the BCR/ABL1 fusion gene, usually resulting from the chromosome rearrangement t(9;22)(q34;q11) or its variants, that leads to constitutive expression of an aberrant tyrosine kinase. These include chronic myeloid leukaemia (CML) and de novo acute leukaemia of both myeloid Ph(+)AML and lymphoid origin Ph(+)ALL. The latter two disorders are clinically aggressive and therapy challenging even in the era of the powerful tyrosine kinase inhibitors. CML is a multistage progressive disease, which if untreated, inevitably ends as fatal acute leukaemia, either myeloid or lymphoid. The latter is often thought to be indistinguishable from Ph(+)ALL, the most common type of ALL in adults. We have identified DNA sequences the imbalances of which appear to be significantly associated with the disease stage and lineage origin in CML and Ph(+)ALL samples. We used array CGH at a resolution of ~2kb to explore hot spot regions obtained from 102 patient samples comprising 92 CML and controls together with 10 Ph(+)ALL and show how Significance Analysis of Microarrays (1) can be used to identify differences in the genome profile of de novo Ph(+)ALL and lymphoid blast transformation of CML. We show that lymphoid blast crisis CML differs significantly from Ph(+)ALL not only due to the presence of 9p deletions but also due to genomic gains in other chromosomes. Furthermore we identify a sub group of Ph(+)ALL with a distinctive genomic profile. Having identified genome regions of potential interest, ranked in order of significance, out of the 100's of thousands of array results, it is then a challenge to design further experiments to evaluate their contribution to the biology of the BCR/ABL positive disease. 1 Tusher V, Tibshirani R, Chu G: Significance analysis of microarrays applied to the ionizing radiation response. Proc Natl Acad Sci U S A 98:5116-5121 (2001). Disclosures: No relevant conflicts of interest to declare.

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Hill, Ronald J. "The U. S. S. R.: Social Change and Party Adaptability." Comparative Politics 17, no. 4 (July 1985): 453. http://dx.doi.org/10.2307/421748.

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Antoine, Michel. "Sources de l'histoire de France en U. R. S. S." Bibliothèque de l'école des chartes 144, no. 2 (1986): 384–87. http://dx.doi.org/10.3406/bec.1986.450426.

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Lee, Eun Pyo, and Seung On Lee. "DOUBLE (r, s)(u, v)-PREOPEN SETS." Journal of the Chungcheong Mathematical Society 29, no. 1 (February 15, 2016): 13–22. http://dx.doi.org/10.14403/jcms.2016.29.1.13.

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Tomoszek, Maxim. "Impeachment in the U. S. Constitution and Practice – Implications for the Czech Constitution." International and Comparative Law Review 17, no. 1 (June 1, 2017): 129–46. http://dx.doi.org/10.2478/iclr-2018-0005.

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SummaryThe goal of this article is to critically evaluate, what role the impeachment plays in the U. S. Constitutional system and how it contributes to ensuring accountability of elected officials in the USA. To this end, the author will provide a short overview of the development of the institution of impeachment, discuss the current regulation of impeachment in the U. S. Constitution and the application of impeachment in practice, assessing its efficiency and role in the constitutional system. Finally, the conclusions will be reflected upon from the viewpoint of the Czech Constitutional system and its model of constitutional accountability.

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11

OMATA, Toshio. "Teaching Points in High School Georaphy of U. S. S. R." New Geography 32, no. 4 (1985): 16–32. http://dx.doi.org/10.5996/newgeo.32.4_16.

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12

Nesmeyanov, A. N., and E. G. Perevalova. "RECENT ADVANCES IN FERROCENE CHEMISTRY IN THE U. S. S. R." Annals of the New York Academy of Sciences 125, no. 1 (December 16, 2006): 67–88. http://dx.doi.org/10.1111/j.1749-6632.1965.tb45379.x.

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13

Fall, Mouhamed Moustapha, and Enrico Valdinoci. "Uniqueness and Nondegeneracy of Positive Solutions of $${(-\Delta)^s u + u = u^p \, {\rm in} \, \mathbb{R}^N}$$ ( - Δ ) s u + u = u p in R N when s is Close to 1." Communications in Mathematical Physics 329, no. 1 (February 28, 2014): 383–404. http://dx.doi.org/10.1007/s00220-014-1919-y.

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14

Solomon, Peter H. "The U. S. S. R. Supreme Court: History, Role, and Future Prospects." American Journal of Comparative Law 38, no. 1 (1990): 127. http://dx.doi.org/10.2307/840257.

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15

Boldyrev, V. V. "Progress in mechanochemistry of inorganic solids in the U. S. S. R." Journal of the Society of Powder Technology, Japan 26, no. 4 (1989): 260–67. http://dx.doi.org/10.4164/sptj.26.260.

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16

Lee, Eun Pyo, and Seung On Lee. "DOUBLE PAIRWISE (r, s)(u, v)-SEMICONTINUOUS MAPPINGS." Journal of the Chungcheong Mathematical Society 27, no. 4 (November 15, 2014): 603–14. http://dx.doi.org/10.14403/jcms.2014.27.4.603.

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17

Benedict, Michael Les, and David E. Kyvig. "Explicit and Authentic Acts: Amending the U. S. Constitution, 1776-1995." American Historical Review 102, no. 4 (October 1997): 1226. http://dx.doi.org/10.2307/2170763.

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18

Vile, John R. "The Long Legacy of Proposals to Rewrite the U. S. Constitution." PS: Political Science and Politics 26, no. 2 (June 1993): 208. http://dx.doi.org/10.2307/419831.

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19

Lofgren, Charles A., and Donald W. Jackson. "Even the Children of Strangers: Equality under the U. S. Constitution." Journal of Southern History 60, no. 1 (February 1994): 153. http://dx.doi.org/10.2307/2210756.

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20

Hall, Kermit L., and David E. Kyvig. "Explicit and Authentic Acts: Amending the U. S. Constitution, 1776-1995." American Journal of Legal History 41, no. 4 (October 1997): 487. http://dx.doi.org/10.2307/846099.

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21

Jing, Naihuan, and Ming Liu. "$$R$$ R -Matrix Realization of Two-Parameter Quantum Group $$U_{r,s}(\mathfrak {gl}_n)$$ U r , s ( gl n )." Communications in Mathematics and Statistics 2, no. 3-4 (December 2014): 211–30. http://dx.doi.org/10.1007/s40304-014-0037-7.

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22

Ferreira, C. P., M. M. Guzzo, and P. C. de Holanda. "Cosmological Bounds of Sterile Neutrinos in a S U(3) C ⊗S U(3) L ⊗S U(3) R ⊗U(1) N Model as Dark Matter Candidates." Brazilian Journal of Physics 46, no. 4 (June 15, 2016): 453–61. http://dx.doi.org/10.1007/s13538-016-0427-2.

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23

Luryi, Yuri I., and Konstantin M. Simis. "U. S. S. R.: The Corrupt Society: The Secret World of Soviet Capitalism." University of Toronto Law Journal 35, no. 2 (1985): 215. http://dx.doi.org/10.2307/825581.

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24

Cone, David C. "R ESCUE FROM THE R UBBLE : U RBAN S EARCH & R ESCUE." Prehospital Emergency Care 4, no. 4 (January 2000): 352–57. http://dx.doi.org/10.1080/10903120090941092.

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25

Dittmar, A., G. Delhomme, C. Collet, C. Deschaumes-Molinaro, and E. Vernet-Maury. "Comparative analysis of electrodermal activity (U, R, Z, S)." International Journal of Psychophysiology 14, no. 2 (February 1993): 120. http://dx.doi.org/10.1016/0167-8760(93)90147-h.

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26

Paul, Annegret. "First Occurrence for the Dual Pairs (U(p, q), U(r, s))." Canadian Journal of Mathematics 51, no. 3 (June 1, 1999): 636–57. http://dx.doi.org/10.4153/cjm-1999-029-6.

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27

Sanjian, Andrea Stevenson. "Constraints on Modernization: The Case of Administrative Theory in the U. S. S. R." Comparative Politics 18, no. 2 (January 1986): 193. http://dx.doi.org/10.2307/421843.

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28

Quayle, Matthew. "What the U. S. Constitution Means to Me and to Our Country." Human Rights Quarterly 10, no. 1 (February 1988): 122. http://dx.doi.org/10.2307/761977.

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29

Stephens, Larry. "A Little Rebellion Now and Then: Prologue to the U. S. Constitution." History Teacher 20, no. 2 (February 1987): 293. http://dx.doi.org/10.2307/493036.

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30

Ramrattan, Lall B. "Dealership Competition in the U. S. Automobile Industry." American Economist 45, no. 1 (March 2001): 33–45. http://dx.doi.org/10.1177/056943450104500103.

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This paper develops a model of dealership rivalry for the U.S. auto industry in line with the research program of Joe Bain. In Bain's research, the literature depicts the auto industry as a differentiated oligopoly with non-price competition and price collusion. It has established advertising and R&D rivalry successfully, but has focused little attention to dealership competition. Because Bain has given a dominant role to dealership competition, this paper addresses the dealership rivalry problem. We found that a competitive model allowing a firm to react to a rival's past levels of advertising, R&D outlays, and the number of dealers, represents the firms' non-price competitive behavior well for the 1970–1996 period. The hypotheses we used have captured the joint effects of advertising, R&D, and dealerships, when explicit specifications for the financial constraints facing the firms are accounted for. We are able to statistically validate the hypothesis that U.S. firms do compete in dealership systems, as Joe Bain has predicted, within the differentiated oligopoly market structure. The results also allow some inferences regarding the sequential nature of non-price competition among the firms.

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31

Bişgin, Mustafa Cemil. "Almost convergent sequence spaces derived by the domain of quadruple band matrix." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 19, no. 1 (December 1, 2020): 155–70. http://dx.doi.org/10.2478/aupcsm-2020-0012.

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AbstractIn this work, we construct the sequence spaces f(Q(r, s, t, u)), f0(Q(r, s, t, u)) and fs(Q(r, s, t, u)), where Q(r, s, t, u) is quadruple band matrix which generalizes the matrices Δ3, B(r, s, t), Δ2, B(r, s) and Δ, where Δ3, B(r, s, t), Δ2, B(r, s) and Δ are called third order difference, triple band, second order difference, double band and difference matrix, respectively. Also, we prove that these spaces are BK-spaces and are linearly isomorphic to the sequence spaces f, f0 and fs, respectively. Moreover, we give the Schauder basis and β, γ-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.

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32

Marisetti Sowjanya, Radha Rani Tammileti, Gangadhara Rao Ankata,. "f-Primary Ideals in Semigroups." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 5 (April 11, 2021): 857–61. http://dx.doi.org/10.17762/turcomat.v12i5.1495.

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Right now, the terms left f-Primary Ideal, right f-Primary Idealand f- primary ideals are presented. It is Shown that An ideal U in a semigroup S fulfills the condition that If G, H are two ideals of S with the end goal that f (G) f (H)⊆U and f(H)⊈U then f(G)⊆rf (U)iff f (q), f (r)⊆S , <f (q)><f (r)>⊆U and f (r)⊈U then f (q)⊆rf (U) in like manner it is exhibited that An ideal U out of a semigroup S fulfills condition If G, H are two ideals of S such that f (G) f (H)⊆U and f (G)⊈U then f (H) ⊆rf (U) iff f (q), f (r)⊆S,<f (q)><f (r)>⊆U and f (q)⊈U⇒f (r)⊆rf (U). By utilizing the meanings of left - f- primary and right f- primary ideals a couple of conditions are illustrated It is shown that J is a restrictive maximal ideal in Son the off chance thatrf (U) = J for some ideal U in S at that point J will be a f- primary ideal and Jn is f-primary ideal for some n it is explained that if S is quasi-commutative then an ideal U of S is left f - primary iff right f -primary.

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Kassim A. Jassim and Ali Kareem Kadhim. "Generalized Left Jordan ideals In Prime Rings." journal of the college of basic education 17, no. 72 (June 17, 2019): 87–92. http://dx.doi.org/10.35950/cbej.v17i72.4500.

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Let R be a prime ring and U be a (σ,τ)-left Jordan ideal .Then in this paper, we proved the following , if aU Z (Ua Z), a R, then a = 0 or U Z. If aU C s,t (Ua C s,t), a R, then either a = 0 or U Z. If 0 ≠ [U,U] s,t .Then U Z. If 0≠[U,U] s,t C s,t, then U Z .Also, we checked the converse some of these theorems and showed that are not true, so we give an example for them.

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34

Meng, Yuxi, Xinrui Zhang, and Xiaoming He. "Ground state solutions for a class of fractional Schrodinger-Poisson system with critical growth and vanishing potentials." Advances in Nonlinear Analysis 10, no. 1 (January 1, 2021): 1328–55. http://dx.doi.org/10.1515/anona-2020-0179.

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Abstract In this paper, we study the fractional Schrödinger-Poisson system ( − Δ ) s u + V ( x ) u + K ( x ) ϕ | u | q − 2 u = h ( x ) f ( u ) + | u | 2 s ∗ − 2 u , in R 3 , ( − Δ ) t ϕ = K ( x ) | u | q , in R 3 , $$\begin{array}{} \displaystyle \left\{ \begin{array}{ll} (-{\it\Delta})^{s}u+V(x)u+ K(x) \phi|u|^{q-2}u=h(x)f(u)+|u|^{2^{\ast}_{s}-2}u,&\mbox{in}~ {\mathbb R^{3}},\\ (-{\it\Delta})^{t}\phi=K(x)|u|^{q},&\mbox{in}~ {\mathbb R^{3}}, \end{array}\right. \end{array}$$ where s, t ∈ (0, 1), 3 < 4s < 3 + 2t, q ∈ (1, 2 s ∗ $\begin{array}{} \displaystyle 2^*_s \end{array}$ /2) are real numbers, (−Δ) s stands for the fractional Laplacian operator, 2 s ∗ := 6 3 − 2 s $\begin{array}{} \displaystyle 2^{*}_{s}:=\frac{6}{3-2s} \end{array}$ is the fractional critical Sobolev exponent, K, V and h are non-negative potentials and V, h may be vanish at infinity. f is a C 1-function satisfying suitable growth assumptions. We show that the above fractional Schrödinger-Poisson system has a positive and a sign-changing least energy solution via variational methods.

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35

Isernia, Teresa. "Fractional p&q-Laplacian problems with potentials vanishing at infinity." Opuscula Mathematica 40, no. 1 (2020): 93–110. http://dx.doi.org/10.7494/opmath.2020.40.1.93.

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In this paper we prove the existence of a positive and a negative ground state weak solution for the following class of fractional $p&q$-Laplacian problems \[\begin{aligned} (-\Delta)_{p}^{s} u + (-\Delta)_{q}^{s} u + V(x) (|u|^{p-2}u + |u|^{q-2}u)= K(x) f(u) \quad \text{ in } \mathbb{R}^{N},\end{aligned}\] where $s\in (0, 1)$, $1\lt p\lt q \lt\frac{N}{s}$, $V: \mathbb{R}^{N}\to \mathbb{R}$ and $K: \mathbb{R}^{N}\to \mathbb{R}$ are continuous, positive functions, allowed for vanishing behavior at infinity, $f$ is a continuous function with quasicritical growth and the leading operator $(-\Delta)^{s}_{t}$, with $t\in \{p,q\}$, is the fractional $t$-Laplacian operator.

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36

Kim, Jae-Myoung, Yun-Ho Kim, and Jongrak Lee. "Multiplicity of Small or Large Energy Solutions for Kirchhoff–Schrödinger-Type Equations Involving the Fractional p-Laplacian in RN." Symmetry 10, no. 10 (September 26, 2018): 436. http://dx.doi.org/10.3390/sym10100436.

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We herein discuss the following elliptic equations: M ∫ R N ∫ R N | u ( x ) - u ( y ) | p | x - y | N + p s d x d y ( - Δ ) p s u + V ( x ) | u | p - 2 u = λ f ( x , u ) i n R N , where ( - Δ ) p s is the fractional p-Laplacian defined by ( - Δ ) p s u ( x ) = 2 lim ε ↘ 0 ∫ R N ∖ B ε ( x ) | u ( x ) - u ( y ) | p - 2 ( u ( x ) - u ( y ) ) | x - y | N + p s d y , x ∈ R N . Here, B ε ( x ) : = { y ∈ R N : | x - y | < ε } , V : R N → ( 0 , ∞ ) is a continuous function and f : R N × R → R is the Carathéodory function. Furthermore, M : R 0 + → R + is a Kirchhoff-type function. This study has two aims. One is to study the existence of infinitely many large energy solutions for the above problem via the variational methods. In addition, a major point is to obtain the multiplicity results of the weak solutions for our problem under various assumptions on the Kirchhoff function M and the nonlinear term f. The other is to prove the existence of small energy solutions for our problem, in that the sequence of solutions converges to 0 in the L ∞ -norm.

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37

Gangloff, Tilmann P. "Neuer Anlauf für den Jugendmedien- s c h u t z - S t a a t s v e r t r a g." Jugend Medien Schutz-Report 38, no. 5 (2015): 6–8. http://dx.doi.org/10.5771/0170-5067-2015-5-6.

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38

Dębicki, Krzysztof, Enkelejd Hashorva, and Natalia Soja-Kukieła. "Extremes of Homogeneous Gaussian Random Fields." Journal of Applied Probability 52, no. 01 (March 2015): 55–67. http://dx.doi.org/10.1017/s0021900200012195.

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Let {X(s, t): s, t ≥ 0} be a centred homogeneous Gaussian field with almost surely continuous sample paths and correlation function r(s, t) = cov(X(s, t), X(0, 0)) such that r(s, t) = 1 - |s|α1 - |t|α2 + o(|s|α1 + |t|α2 ), s, t → 0, with α1, α2 ∈ (0, 2], and r(s, t) < 1 for (s, t) ≠ (0, 0). In this contribution we derive an asymptotic expansion (as u → ∞) of P(sup(sn 1(u),tn 2(u)) ∈[0,x]∙[0,y] X(s, t) ≤ u), where n 1(u)n 2(u) = u 2/α1+2/α2 Ψ(u), which holds uniformly for (x, y) ∈ [A, B]2 with A, B two positive constants and Ψ the survival function of an N(0, 1) random variable. We apply our findings to the analysis of extremes of homogeneous Gaussian fields over more complex parameter sets and a ball of random radius. Additionally, we determine the extremal index of the discretised random field determined by X(s, t).

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39

Pucci, Patrizia, Mingqi Xiang, and Binlin Zhang. "Existence results for Schrödinger–Choquard–Kirchhoff equations involving the fractional p-Laplacian." Advances in Calculus of Variations 12, no. 3 (July 1, 2019): 253–75. http://dx.doi.org/10.1515/acv-2016-0049.

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AbstractThe paper is concerned with existence of nonnegative solutions of a Schrödinger–Choquard–Kirchhoff-type fractional p-equation. As a consequence, the results can be applied to the special case(a+b\|u\|_{s}^{p(\theta-1)})[(-\Delta)^{s}_{p}u+V(x)|u|^{p-2}u]=\lambda f(x,u)% +\Bigg{(}\int_{\mathbb{R}^{N}}\frac{|u|^{p_{\mu,s}^{*}}}{|x-y|^{\mu}}\,dy% \Biggr{)}|u|^{p_{\mu,s}^{*}-2}u\quad\text{in }\mathbb{R}^{N},where\|u\|_{s}=\Bigg{(}\iint_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^{p}}{|x-y|^{N+ps}}% \,dx\,dy+\int_{\mathbb{R}^{N}}V(x)|u|^{p}\,dx\Biggr{)}^{\frac{1}{p}},{a,b\in\mathbb{R}^{+}_{0}}, with {a+b>0}, {\lambda>0} is a parameter, {s\in(0,1)}, {N>ps}, {\theta\in[1,N/(N-ps))}, {(-\Delta)^{s}_{p}} is the fractional p-Laplacian, {V:\mathbb{R}^{N}\rightarrow\mathbb{R}^{+}} is a potential function, {0<\mu<N}, {p_{\mu,s}^{*}=(pN-p\mu/2)/(N-ps)} is the critical exponent in the sense of Hardy–Littlewood–Sobolev inequality, and {f:\mathbb{R}^{N}\times\mathbb{R}\rightarrow\mathbb{R}} is a Carathéodory function. First, via the Mountain Pass theorem, existence of nonnegative solutions is obtained when f satisfies superlinear growth conditions and λ is large enough. Then, via the Ekeland variational principle, existence of nonnegative solutions is investigated when f is sublinear at infinity and λ is small enough. More intriguingly, the paper covers a novel feature of Kirchhoff problems, which is the fact that the parameter a can be zero. Hence the results of the paper are new even for the standard stationary Kirchhoff problems.

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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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41

Dębicki, Krzysztof, Enkelejd Hashorva, and Natalia Soja-Kukieła. "Extremes of Homogeneous Gaussian Random Fields." Journal of Applied Probability 52, no. 1 (March 2015): 55–67. http://dx.doi.org/10.1239/jap/1429282606.

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Let {X(s, t): s, t ≥ 0} be a centred homogeneous Gaussian field with almost surely continuous sample paths and correlation function r(s, t) = cov(X(s, t), X(0, 0)) such that r(s, t) = 1 - |s|α1 - |t|α2 + o(|s|α1 + |t|α2), s, t → 0, with α1, α2 ∈ (0, 2], and r(s, t) < 1 for (s, t) ≠ (0, 0). In this contribution we derive an asymptotic expansion (as u → ∞) of P(sup(sn1(u),tn2(u)) ∈[0,x]∙[0,y]X(s, t) ≤ u), where n1(u)n2(u) = u2/α1+2/α2Ψ(u), which holds uniformly for (x, y) ∈ [A, B]2 with A, B two positive constants and Ψ the survival function of an N(0, 1) random variable. We apply our findings to the analysis of extremes of homogeneous Gaussian fields over more complex parameter sets and a ball of random radius. Additionally, we determine the extremal index of the discretised random field determined by X(s, t).

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42

He, Yi. "Singularly Perturbed Fractional Schrödinger Equations with Critical Growth." Advanced Nonlinear Studies 18, no. 3 (August 1, 2018): 587–611. http://dx.doi.org/10.1515/ans-2018-2017.

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AbstractWe are concerned with the following singularly perturbed fractional Schrödinger equation:\left\{\begin{aligned} &\displaystyle{\varepsilon^{2s}}{(-\Delta)^{s}}u+V(x)u=% f(u)&&\displaystyle{\text{in }}{\mathbb{R}^{N}},\\ &\displaystyle u\in{H^{s}}({\mathbb{R}^{N}}),&&\displaystyle u>0{\text{ on }}{% \mathbb{R}^{N}},\end{aligned}\right.where ε is a small positive parameter,{N>2s}, and{{(-\Delta)^{s}}}, with{s\in(0,1)}, is the fractional Laplacian. Using variational technique, we construct a family of positive solutions{{u_{\varepsilon}}\in{H^{s}}({\mathbb{R}^{N}})}which concentrates around the local minima ofVas{\varepsilon\to 0}under general conditions onfwhich we believe to be almost optimal.

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43

Gerow, Edwin, G. Bongard-Levin, and A. Vigasin. "The Image of India: The Study of Ancient Indian Civilisation in the U. S. S. R." Journal of the American Oriental Society 107, no. 2 (April 1987): 360. http://dx.doi.org/10.2307/602866.

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44

Wagner, W. J., and Maria Los. "Communist Ideology, Law and Crime: A Comparative View of the U. S. S. R. and Poland." American Journal of Comparative Law 37, no. 4 (1989): 841. http://dx.doi.org/10.2307/840232.

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45

Han, Qi. "Compact Sobolev-Slobodeckij embeddings and positive solutions to fractional Laplacian equations." Advances in Nonlinear Analysis 11, no. 1 (September 4, 2021): 432–53. http://dx.doi.org/10.1515/anona-2020-0133.

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Abstract In this work, we study the existence of a positive solution to an elliptic equation involving the fractional Laplacian (−Δ) s in ℝ n , for n ≥ 2, such as (0.1) ( − Δ ) s u + E ( x ) u + V ( x ) u q − 1 = K ( x ) f ( u ) + u 2 s ⋆ − 1 . $$(-\Delta)^{s} u+E(x) u+V(x) u^{q-1}=K(x) f(u)+u^{2_{s}^{\star}-1}.$$ Here, s ∈ (0, 1), q ∈ 2 , 2 s ⋆ $q \in\left[2,2_{s}^{\star}\right)$ with 2 s ⋆ := 2 n n − 2 s $2_{s}^{\star}:=\frac{2 n}{n-2 s}$ being the fractional critical Sobolev exponent, E(x), K(x), V(x) > 0 : ℝ n → ℝ are measurable functions which satisfy joint “vanishing at infinity” conditions in a measure-theoretic sense, and f (u) is a continuous function on ℝ of quasi-critical, super-q-linear growth with f (u) ≥ 0 if u ≥ 0. Besides, we study the existence of multiple positive solutions to an elliptic equation in ℝ n such as (0.2) ( − Δ ) s u + E ( x ) u + V ( x ) u q − 1 = λ K ( x ) u r − 1 , $$(-\Delta)^{s} u+E(x) u+V(x) u^{q-1}=\lambda K(x) u^{r-1},$$ where 2 < r < q < ∞(both possibly (super-)critical), E(x), K(x), V(x) > 0 : ℝ n → ℝ are measurable functions satisfying joint integrability conditions, and λ > 0 is a parameter. To study (0.1)-(0.2), we first describe a family of general fractional Sobolev-Slobodeckij spaces Ms ;q,p (ℝ n ) as well as their associated compact embedding results.

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46

Etingof, P., P. Malcolmson, and F. Okoh. "Root Extensions and Factorization in Affine Domains." Canadian Mathematical Bulletin 53, no. 2 (June 1, 2010): 247–55. http://dx.doi.org/10.4153/cmb-2010-014-8.

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AbstractAn integral domain R is IDPF (Irreducible Divisors of Powers Finite) if, for every non-zero element a in R, the ascending chain of non-associate irreducible divisors in R of an stabilizes on a finite set as n ranges over the positive integers, while R is atomic if every non-zero element that is not a unit is a product of a finite number of irreducible elements (atoms). A ring extension S of R is a root extension or radical extension if for each s in S, there exists a natural number n(s) with sn(s) in R. In this paper it is shown that the ascent and descent of the IDPF property and atomicity for the pair of integral domains (R, S) is governed by the relative sizes of the unit groups U(R) and U(S) and whether S is a root extension of R. The following results are deduced from these considerations: An atomic IDPF domain containing a field of characteristic zero is completely integrally closed. An affine domain over a field of characteristic zero is IDPF if and only if it is completely integrally closed. Let R be a Noetherian domain with integral closure S. Suppose the conductor of S into R is non-zero. Then R is IDPF if and only if S is a root extension of R and U(S)/U(R) is finite.

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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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Bhakta, Mousomi, Souptik Chakraborty, and Patrizia Pucci. "Fractional Hardy-Sobolev equations with nonhomogeneous terms." Advances in Nonlinear Analysis 10, no. 1 (January 1, 2021): 1086–116. http://dx.doi.org/10.1515/anona-2020-0171.

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Abstract This paper deals with existence and multiplicity of positive solutions to the following class of nonlocal equations with critical nonlinearity: ( − Δ ) s u − γ u | x | 2 s = K ( x ) | u | 2 s ∗ ( t ) − 2 u | x | t + f ( x ) in R N , u ∈ H ˙ s ( R N ) , $$\begin{array}{} \displaystyle \begin{cases} (-{\it\Delta})^s u -\gamma\dfrac{u}{|x|^{2s}}=K(x)\dfrac{|u|^{2^*_s(t)-2}u}{|x|^t}+f(x) \quad\mbox{in}\quad\mathbb R^N,\\ \qquad\qquad\qquad\quad u\in \dot{H}^s(\mathbb R^N), \end{cases} \end{array}$$ where N > 2s, s ∈ (0, 1), 0 ≤ t < 2s < N and 2 s ∗ ( t ) := 2 ( N − t ) N − 2 s $\begin{array}{} \displaystyle 2^*_s(t):=\frac{2(N-t)}{N-2s} \end{array}$ . Here 0 < γ < γ N,s and γ N,s is the best Hardy constant in the fractional Hardy inequality. The coefficient K is a positive continuous function on ℝ N , with K(0) = 1 = lim|x|→∞ K(x). The perturbation f is a nonnegative nontrivial functional in the dual space Ḣs (ℝ N )′ of Ḣs (ℝ N ). We establish the profile decomposition of the Palais-Smale sequence associated with the functional. Further, if K ≥ 1 and ∥f∥(Ḣs )′ is small enough (but f ≢ 0), we establish existence of at least two positive solutions to the above equation.

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Ambrosio, Vincenzo. "Multiple Solutions for Superlinear Fractional Problems via Theorems of Mixed Type." Advanced Nonlinear Studies 18, no. 4 (November 1, 2018): 799–817. http://dx.doi.org/10.1515/ans-2018-0006.

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AbstractIn this paper, we investigate the existence of multiple solutions for the following two fractional problems:\left\{\begin{aligned} \displaystyle(-\Delta_{\Omega})^{s}u-\lambda u&% \displaystyle=f(x,u)&&\displaystyle\text{in }\Omega,\\ \displaystyle u&\displaystyle=0&&\displaystyle\text{in }\partial\Omega\end{% aligned}\right.\qquad\text{and}\qquad\left\{\begin{aligned} \displaystyle(-% \Delta_{\mathbb{R}^{N}})^{s}u-\lambda u&\displaystyle=f(x,u)&&\displaystyle% \text{in }\Omega,\\ \displaystyle u&\displaystyle=0&&\displaystyle\text{in }\mathbb{R}^{N}% \setminus\Omega,\end{aligned}\right.where{s\in(0,1)},{N>2s}, Ω is a smooth bounded domain of{\mathbb{R}^{N}}, and{f:\bar{\Omega}\times\mathbb{R}\to\mathbb{R}}is a superlinear continuous function which does not satisfy the well-known Ambrosetti–Rabinowitz condition. Here{(-\Delta_{\Omega})^{s}}is the spectral Laplacian and{(-\Delta_{\mathbb{R}^{N}})^{s}}is the fractional Laplacian in{\mathbb{R}^{N}}. By applying variational theorems of mixed type due to Marino and Saccon and the Linking Theorem, we prove the existence of multiple solutions for the above problems.

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50

Ma, Ruyun, Chunjie Xie, and Abubaker Ahmed. "Positive Solutions of the One-Dimensional p-Laplacian with Nonlinearity Defined on a Finite Interval." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/492026.

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We use the quadrature method to show the existence and multiplicity of positive solutions of the boundary value problems involving one-dimensional p-Laplacian u′t|p−2u′t′+λfut=0, t∈0,1, u(0)=u(1)=0, where p∈(1,2], λ∈(0,∞) is a parameter, f∈C1([0,r),[0,∞)) for some constant r>0, f(s)>0 in (0,r), and lims→r-(r-s)p-1f(s)=+∞.

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