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Journal articles on the topic 'P^2q'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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1

Hernández Iglesias, Mauro Fernando. "Singularidad de la polar de una curva plana irreducible en K(2p,2q,2pq+d)." Pesquimat 22, no. 1 (May 3, 2019): 1–8. http://dx.doi.org/10.15381/pes.v22i1.15758.

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Veremos que existe un abierto de Zariski en el conjunto de curvas planas irreducibles con exponentes característicos 2p; 2q y 2q+d, dado por K(2p; 2q; 2q+d) con mcd{p,q} = 1 y d impar, donde la polar es no degenerada, su topología es constante y determinada apenas por p y q.

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2

Asbullah, Muhammad Asyraf, Normahirah Nek Abd Rahman, uhammad Rezal Kamel Ariffin, Siti Hasana Sapar, and Faridah Yunos. "CRYPTANALYSIS OF RSA KEY EQUATION OF N=p^2q FOR SMALL |2q – p| USING CONTINUED FRACTION." Malaysian Journal of Science 39, no. 1 (February 29, 2020): 72–80. http://dx.doi.org/10.22452/mjs.vol39no1.6.

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3

Yaying, Taja, Bipan Hazarika, and S. A. Mohiuddine. "Domain of Padovan q-difference matrix in sequence spaces lp and l∞." Filomat 36, no. 3 (2022): 905–19. http://dx.doi.org/10.2298/fil2203905y.

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In this study, we construct the difference sequence spaces lp (P?2q) = (lp)P?2q, 1 ? p ? ?, where P = (?rs) is an infinite matrix of Padovan numbers %s defined by ?rs = {?s/?r+5-2 0 ? s ? r, 0 s > r. and ?2q is a q-difference operator of second order. We obtain some inclusion relations, topological properties, Schauder basis and ?-, ?- and ?-duals of the newly defined space. We characterize certain matrix classes from the space lp (P?2q) to any one of the space l1, c0, c or l?. We examine some geometric properties and give certain estimation for von-Neumann Jordan constant and James constant of the space lp(P). Finally, we estimate upper bound for Hausdorff matrix as a mapping from lp to lp(P).

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Zhao, Xin, and Wenming Zou. "On a class of critical elliptic systems in ℝ4." Advances in Nonlinear Analysis 10, no. 1 (September 13, 2020): 548–68. http://dx.doi.org/10.1515/anona-2020-0136.

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Abstract In the present paper, we consider the following classes of elliptic systems with Sobolev critical growth: $$\begin{array}{} \displaystyle \begin{cases} -{\it\Delta} u+\lambda_1u=\mu_1 u^3+\beta uv^2+\frac{2q}{p} y u^{\frac{2q}{p}-1}v^2\quad &\hbox{in}\;{\it\Omega}, \\ -{\it\Delta} v+\lambda_2v=\mu_2 v^3+\beta u^2v+2 y u^{\frac{2q}{p}}v\quad&\hbox{in}\;{\it\Omega}, \\ u,v \gt 0&\hbox{in}\;{\it\Omega}, \\ u,v=0&\hbox{on}\;\partial{\it\Omega}, \end{cases} \end{array}$$ where Ω ⊂ ℝ4 is a smooth bounded domain with smooth boundary ∂Ω; p, q are positive coprime integers with 1 < $\begin{array}{} \displaystyle \frac{2q}{p} \end{array}$ < 2; μi > 0 and λi ∈ ℝ are fixed constants, i = 1, 2; β > 0, y > 0 are two parameters. We prove a nonexistence result and the existence of the ground state solution to the above system under proper assumptions on the parameters. It seems that this system has not been explored directly before.

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5

ALZER, HORST. "ON AN INTEGRAL INEQUALITY OF R. BELLMAN." Tamkang Journal of Mathematics 22, no. 2 (June 1, 1991): 187–91. http://dx.doi.org/10.5556/j.tkjm.22.1991.4597.

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We prove: if $u$ and $v$ are non-negative, concave functions defined on $[0, 1]$ satisfying \[\int_0^1 (u(x))^{2p} dx =\int_0^1 (v(x))^{2q} dx=1, \quad p>0, \quad q>0,\] then \[\int_0^1(u(x))^p (v(x))^q dx\ge\frac{2\sqrt{(2p+1)(2q+1)}}{(p+1)(q+1)}-1.\]

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6

Kamaraj, T., and J. Thangakani. "Edge even and edge odd graceful labelings of Paley Graphs." Journal of Physics: Conference Series 1770, no. 1 (March 1, 2021): 012068. http://dx.doi.org/10.1088/1742-6596/1770/1/012068.

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Abstract Edge even graceful labeling is a novel graceful labelling, introduced in 2017 by Elsonbaty and Daoud. A graph G with p vertices and q edges is called an edge even graceful if there is a bijection f: E(G) → {2, 4,. . ., 2q} such that, when each vertex is assigned the sum of the labels of all edges incident to it mod 2k, where k = max (p, q), the resulting vertex labels are distinct. A labeling of G is called edge odd graceful labeling, if there exists a bijection f from the set of edges E(G) to the set {1,3,5,…,2q-1} such that the induced the map f* from the set of vertices V(G) to {0,1,2,.,.,2q-1} given by f*(u) = Σ uv∈E(G) f(uv) (mod 2q) is an injection. A graph which admits edge even (odd) graceful labeling is called an edge even (odd) graceful graph. Paley graphs are dense undirected graphs raised from the vertices as elements of an appropriate finite field by joining pairs of vertices that differ by a quadratic residue. In this paper, we study the construction of edge even (odd) graceful labeling for Paley graphs and prove that Paley graphs of prime order are edge even (odd) graceful.

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7

Liu, Hailin, Bengong Lou, and Bo Ling. "Tetravalent half-arc-transitive graphs of order $p^2q^2$." Czechoslovak Mathematical Journal 69, no. 2 (February 4, 2019): 391–401. http://dx.doi.org/10.21136/cmj.2019.0335-17.

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8

Aguirre, J., and M. Escobedo. "On the blow-up of solutions of a convective reaction diffusion equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 123, no. 3 (1993): 433–60. http://dx.doi.org/10.1017/s0308210500025828.

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SynopsisWe study the blow-up of positive solutions of the Cauchy problem for the semilinear parabolic equationwhere u is a scalar function of the spatial variable x ∈ ℝN and time t > 0, a ∈ ℝV, a ≠ 0, 1 < p and 1 ≦ q. We show that: (a) if p > 1 and 1 ≦ q ≦ p, there always exist solutions which blow up in finite time; (b) if 1 < q ≦ p ≦ min {1 + 2/N, 1 + 2q/(N + 1)} or if q = 1 and 1 < p ≦ l + 2/N, then all positive solutions blow up in finite time; (c) if q > 1 and p > min {1 + 2/N, 1 + 2q/N + 1)}, then global solutions exist; (d) if q = 1 and p > 1 + 2/N, then global solutions exist.

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Abd Ghafar, Amir Hamzah, and Muhammad Rezal Kamel Ariffin. "SPA on Rabin variant with public key $$N=p^2q$$ N = p 2 q." Journal of Cryptographic Engineering 6, no. 4 (February 10, 2016): 339–46. http://dx.doi.org/10.1007/s13389-016-0118-5.

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10

Firmansah, Fery, and Muhammad Ridlo Yuwono. "Odd Harmonious Labeling on Pleated of the Dutch Windmill Graphs." CAUCHY 4, no. 4 (May 30, 2017): 161. http://dx.doi.org/10.18860/ca.v4i4.4043.

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A graph G(p,q) with p=|V(G)| vertices and q=|E(G)| edges. The graph G(p,q) is said to be odd harmonious if there exist an injection f: V(G)->{0,1,2,...,2q-1} such that the induced function f*: E(G)->{1,2,3,...,2q-1} defined by f*(uv)=f(u)+f(v) which is a bijection and f is said to be odd harmonious labeling of G(p,q). In this paper we prove that pleated of the Dutch windmill graphs C_4^(k)(r) with k>=1 and r>=1 are odd harmonious graph. Moreover, we also give odd harmonious labeling construction for the union pleated of the Dutch windmill graph C_4^(k)(r) union C_4^(k)(r) with k>=1 and r>=1.

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11

MORIWAKI, MASAYASU. "MULTIPLICITY-FREE DECOMPOSITIONS OF THE MINIMAL REPRESENTATION OF THE INDEFINITE ORTHOGONAL GROUP." International Journal of Mathematics 19, no. 10 (November 2008): 1187–201. http://dx.doi.org/10.1142/s0129167x08005084.

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Kazhdan, Kostant, Binegar–Zierau and Kobayashi–Ørsted constructed a distinguished infinite-dimensional irreducible unitary representation π of the indefinite orthogonal group G = O(2p, 2q) for p, q ≥ 1 with p + q > 2, which has the smallest Gelfand–Kirillov dimension 2p + 2q - 3 among all infinite-dimensional irreducible unitary representations of G and hence is called the minimal representation. We consider, for which subgroup G′ of G, the restriction π|G′ is multiplicity-free. We prove that the restriction of π to any subgroup containing the direct product group U(p1) × U(p2) × U(q) for p1, p2 ≥ 1 with p1 + p2 = p is multiplicity-free, whereas the restriction to U(p1) × U(p2) × U(q1) × U(q2) for q1, q2 ≥ 1 with q1 + q2 = q has infinite multiplicities.

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Li, Qiang, and Baoquan Yuan. "A regularity criterion for liquid crystal flows in terms of the component of velocity and the horizontal derivative components of orientation field." AIMS Mathematics 7, no. 3 (2022): 4168–75. http://dx.doi.org/10.3934/math.2022231.

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<abstract><p>In this paper, we establish a regularity criterion for the 3D nematic liquid crystal flows. More precisely, we prove that the local smooth solution $ (u, d) $ is regular provided that velocity component $ u_{3} $, vorticity component $ \omega_{3} $ and the horizontal derivative components of the orientation field $ \nabla_{h}d $ satisfy</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{eqnarray*} \int_{0}^{T}|| u_{3}||_{L^{p}}^{\frac{2p}{p-3}}+||\omega_{3}||_{L^{q}}^{\frac{2q}{2q-3}}+||\nabla_{h} d||_{L^{a}}^{\frac{2a}{a-3}} \mbox{d} t<\infty,\nonumber \\ with\ \ 3< p\leq\infty,\ \frac{3}{2}< q\leq\infty,\ 3< a\leq\infty. \end{eqnarray*} $\end{document} </tex-math></disp-formula></p> </abstract>

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13

Bisgaard, Søren. "The Design and Analysis of 2k–p× 2q–rSplit Plot Experiments." Journal of Quality Technology 32, no. 1 (January 2000): 39–56. http://dx.doi.org/10.1080/00224065.2000.11979970.

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14

李, 世荣. "关于方程|Aut(G)|=p~2q~2的解." Chinese Science Bulletin 40, no. 23 (December 1, 1995): 2124–27. http://dx.doi.org/10.1360/csb1995-40-23-2124.

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15

Damelin, S. B., and D. S. Lubinsky. "Necessary and Sufficient Conditions for Mean Convergence of Lagrange Interpolation for Erdős Weights." Canadian Journal of Mathematics 48, no. 4 (August 1, 1996): 710–36. http://dx.doi.org/10.4153/cjm-1996-037-1.

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AbstractWe investigate mean convergence of Lagrange interpolation at the zeros of orthogonal polynomials pn(W2, x) for Erdös weights W2 = e-2Q. The archetypal example is Wk,α = exp(—Qk,α), whereα > 1, k ≥ 1, and is the k-th iterated exponential. Following is our main result: Let 1 < p < ∞, Δ ∊ ℝ, k > 0. Let Ln[f] denote the Lagrange interpolation polynomial to ƒ at the zeros of pn(W2, x) = pn(e-2Q, x). Then forto hold for every continuous function ƒ: ℝ —> ℝ satisfyingit is necessary and sufficient that

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16

Subramanian, Nagarajan, M. R. Bivin, and Nallaswamy Saivaraju. "The Generalized Non-absolute type of sequence spaces." Boletim da Sociedade Paranaense de Matemática 34, no. 2 (September 30, 2015): 263–74. http://dx.doi.org/10.5269/bspm.v34i1.25674.

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In this paper we introduce the notion of $\lambda_{mn}-\chi^{2}$ and $\Lambda^{2}$ sequences. Further, we introduce the spaces $\left[\chi^{2q\lambda}_{f\mu },\left\|\left(d\left(x_{1},0\right),d\left(x_{2},0\right),\cdots, d\left(x_{n-1},0\right)\right)\right\|_{p}\right]^{\textit{I}\left(F\right)}$ and $\left[\Lambda^{2q\lambda}_{f\mu },\left\|\left(d\left(x_{1},0\right),d\left(x_{2},0\right),\cdots, d\left(x_{n-1},0\right)\right)\right\|_{p}\right]^{\textit{I}\left(F\right)},$ which are of non-absolute type and we prove that these spaces are linearly isomorphic to the spaces $\chi^{2}$ and $\Lambda^{2},$ respectively. Moreover, we establish some inclusion relations between these spaces.

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Damelin, S. B., and D. S. Lubinsky. "Necessary and Sufficient Conditions for Mean Convergence of Lagrange Interpolation for Erdős Weights II." Canadian Journal of Mathematics 48, no. 4 (August 1, 1996): 737–57. http://dx.doi.org/10.4153/cjm-1996-038-9.

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AbstractWe complete our investigations of mean convergence of Lagrange interpolation at the zeros of orthogonal polynomials pn(W2, x) for Erdős weights W2 = e-2Q. The archetypal example is Wk,α = exp(—Qk,α), whereα > 1, k ≥ 1, and is the k-th iterated exponential. Following is our main result: Let 1 < p < 4 and α ∊ ℝ Let Ln[f] denote the Lagrange interpolation polynomial to ƒ at the zeros of pn(W2, x) = pn(e-2Q, x). Then forto hold for every continuous function ƒ:ℝ. —> ℝ satisfyingit is necessary and sufficient that α > 1/p. This is, essentially, an extension of the Erdös-Turan theorem on L2 convergence. In an earlier paper, we analyzed convergence for all p > 1, showing the necessity and sufficiency of using the weighting factor 1 + Q for all p > 4. Our proofs of convergence are based on converse quadrature sum estimates, that are established using methods of H. König.

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Kim, Youngjoon, Youngho Kim, and Jeong Seop Sim. "An Improved Order-Preserving Pattern Matching Algorithm Using Fingerprints." Mathematics 10, no. 12 (June 7, 2022): 1954. http://dx.doi.org/10.3390/math10121954.

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Two strings of the same length are order isomorphic if their relative orders are the same. The order-preserving pattern matching problem is to find all substrings of text T that are order isomorphic to pattern P when T(|T|=n) and P(|P|=m) are given. An O(mn+nqlogq+q!)-time algorithm using the O(m+q!) space for the order-preserving pattern matching problem has been proposed utilizing fingerprints of q-grams based on the factorial number system and the bad character heuristic. In this paper, we propose an O(mn+2q)-time algorithm using the O(m+2q) space for the order-preserving pattern matching problem, but utilizing fingerprints of q-grams converted to binary numbers. A comparative experiment using three types of time series data demonstrates that the proposed algorithm is faster than existing algorithms because it reduces the number of order isomorphism tests.

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Agdgomelashvili, Zurab. "Some interesting tasks from the classical number theory." Works of Georgian Technical University, no. 4(518) (December 15, 2020): 150–88. http://dx.doi.org/10.36073/1512-0996-2020-4-150-188.

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The article considers the following issues: – It’s of great interest for p and q primes to determine the number of those prime number divisors of a number 1 1 pq A p    that are less than p. With this purpose we have considered: Theorem 1. Let’s p and q are odd prime numbers and p  2q 1. Then from various individual divisors of the 1 1 pq A p    number, only one of them is less than p. A has at least two different simple divisors; Theorem 2. Let’s p and q are odd prime numbers and p  2q 1. Then all prime divisors of the number 1 1 pq A p    are greater than p; Theorem 3. Let’s q is an odd prime number, and p N \{1}, p]1;q] [q  2; 2q] , then each of the different prime divisors of the number 1 1 pq A p    taken separately is greater than p; Theorem 4. Let’s q is an odd prime number, and p{q1; 2q1}, then from different prime divisors of the number 1 1 pq A p    taken separately, only one of them is less than p. A has at least two different simple divisors. Task 1. Solve the equation 1 2 1 z x y y    in the natural numbers x , y, z. In addition, y must be a prime number. Task 2. Solve the equation 1 3 1 z x y y    in the natural numbers x , y, z. In addition, y must be a prime number. Task 3. Solve the equation 1 1 z x y p y    where p{6; 7; 11; 13;} are the prime numbers, x, y  N and y is a prime number. There is a lema with which the problem class can be easily solved: Lemma ●. Let’s a, b, nN and (a,b) 1. Let’s prove that if an  0 (mod| ab|) , or bn  0 (mod| ab|) , then | ab|1. Let’s solve the equations ( – ) in natural x , y numbers: I. 2 z x y z z x y          ; VI. (x  y)xy  x y ; II. (x  y)z  (2x)z  yz ; VII. (x  y)xy  yx ; III. (x  y)z  (3x)z  yz ; VIII. (x  y) y  (x  y)x , (x  y) ; IV. ( y  x)x y  x y , (y  x) ; IX. (x  y)x y  xxy ; V. ( y  x)x y  yx , (y  x) ; X. (x  y)xy  (x  y)x , (y  x) . Theorem . If a, bN (a,b) 1, then each of the divisors (a2  ab  b2 ) will be similar. The concept of pseudofibonacci numbers is introduced and some of their properties are found.

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Cahen, M., A. Franc, and S. Gutt. "Spectrum of the Dirac operator on complex projective space P 2q-1(?)." Letters in Mathematical Physics 18, no. 2 (August 1989): 165–76. http://dx.doi.org/10.1007/bf00401871.

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21

Rottey, Sara, and Geertrui Van de Voorde. "Unitals with many Baer secants through a fixed point." Advances in Geometry 19, no. 1 (January 28, 2019): 21–30. http://dx.doi.org/10.1515/advgeom-2017-0010.

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Abstract We show that a unital U in PG(2, q2) containing a point P, such that at least q2 − ϵ of the secant lines through P intersect U in a Baer subline, is an ovoidal Buekenhout–Metz unital (where ϵ ≈ 2q for q even and ϵ ≈ q3/2/2 for q odd).

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22

MADETI, PRABHAKAR, and RAMA MISHRA. "MINIMAL DEGREE SEQUENCE FOR TORUS KNOTS OF TYPE (p, q)." Journal of Knot Theory and Its Ramifications 18, no. 04 (April 2009): 485–91. http://dx.doi.org/10.1142/s021821650900704x.

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In this paper we prove the following result: for coprime positive integers p and q with p < q, if r is the least positive integer such that 2p-1 and q + r are coprime, then the minimal degree sequence for a torus knot of type (p, q) is the triple (2p - 1, q + r, d) or (q + r, 2p - 1, d) where q + r + 1 ≤ d ≤ 2q - 1.

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23

Khmaladze, Estáte V. "Convergence Properties in Certain Occupancy Problems Including the Karlin-Rouault Law." Journal of Applied Probability 48, no. 4 (December 2011): 1095–113. http://dx.doi.org/10.1239/jap/1324046021.

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Let x denote a vector of length q consisting of 0s and 1s. It can be interpreted as an ‘opinion’ comprised of a particular set of responses to a questionnaire consisting of q questions, each having {0, 1}-valued answers. Suppose that the questionnaire is answered by n individuals, thus providing n ‘opinions’. Probabilities of the answer 1 to each question can be, basically, arbitrary and different for different questions. Out of the 2q different opinions, what number, μn, would one expect to see in the sample? How many of these opinions, μn(k), will occur exactly k times? In this paper we give an asymptotic expression for μn / 2q and the limit for the ratios μn(k)/μn, when the number of questions q increases along with the sample size n so that n = λ2q, where λ is a constant. Let p(x) denote the probability of opinion x. The key step in proving the asymptotic results as indicated is the asymptotic analysis of the joint behaviour of the intensities np(x). For example, one of our results states that, under certain natural conditions, for any z > 0, ∑1{np(x) > z} = dnz−u, dn = o(2q).

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Numasawa, H., N. Yamamoto, and T. Shibahara. "P.42 Loss of heterozygosity on chromosome 2q inhuman oral squamous cell carcinoma." Oral Oncology Supplement 1, no. 1 (January 2005): 158. http://dx.doi.org/10.1016/s1744-7895(05)80406-7.

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Anderson, G. D., S. Banerjee, and C. S. David. "MHC class II A alpha and E alpha molecules determine the clonal deletion of V beta 6+ T cells. Studies with recombinant and transgenic mice." Journal of Immunology 143, no. 11 (December 1, 1989): 3757–61. http://dx.doi.org/10.4049/jimmunol.143.11.3757.

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Abstract Interactions between MHC class II genes and minor lymphocyte stimulating (Mls) associated products are responsible for clonally deleting self-reactive T cells in mice. Here we demonstrate the role of the intact I-A and I-E molecules as well as the individual A alpha and E alpha chains in the deletion of cells bearing the V beta 6 TCR. DBA/1 (H-2q, Mls-1a) mice were crossed with various inbred congenic, recombinant, and transgenic strains and the F1's were screened for V beta 6 expression. All I-E+ strains were fully permissive in deleting V beta 6+ T cells. I-E- strains expressing I-A b,f,s,k,p permitted only partial deletion, while I-Aq strains showed no deletion. Recombinant I-Aq and I-Af strains which expressed E kappa alpha chain in the absence of E beta chain showed a decrease in V beta 6+ T cells as compared to their H-2q and H-2f counterparts. Furthermore, transgenic mice expressing E kappa alpha Aq beta gene in an H-2q haplotype (E kappa alpha Aq beta?) gave similar results to that of the recombinants in deleting V beta 6 T-cells. The role of the 1-A molecule was also shown by the partial deletion of V beta 6+ T cells in H-2q mice expressing transgenic I-Ak molecules. These results demonstrate that the E alpha chain is important in the deletion of V beta 6 T-cells in Mls-1a mice. The role of A alpha chain is also implied by the permissiveness of E kappa alpha Aq beta but not Aq alpha Aq beta molecules in the deletion of V beta 6+ T cells.

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Geng, Fengjie, and Hairong Lian. "Bifurcation of Limit Cycles from a Quasi-Homogeneous Degenerate Center." International Journal of Bifurcation and Chaos 25, no. 01 (January 2015): 1550007. http://dx.doi.org/10.1142/s0218127415500078.

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In this paper, we deal with the following differential system [Formula: see text] where p, q are positive integers, and P(x, y), Q(x, y) are real polynomials of degree n, we obtain an upper bound for the maximum number of limit cycles bifurcating from the period annulus of a quasi-homogeneous center, that is (n - 1)p1 + (t + 1)q - 1 + 2rp1q1(q + 3) + 2tqrp1q1, where t = [n/2q] + 2, (p, q) = r(p1, q1), p1 and q1 are coprime.

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Kajiura, Hiroshige. "Cyclicity in homotopy algebras and rational homotopy theory." Georgian Mathematical Journal 25, no. 4 (December 1, 2018): 545–70. http://dx.doi.org/10.1515/gmj-2018-0058.

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AbstractKadeishvili proposes a minimal{C_{\infty}}-algebra as a rational homotopy model of a space. We discuss a cyclic version of this Kadeishvili{C_{\infty}}-model and apply it to classifying rational Poincaré duality spaces. We classify 1-connected minimal cyclic{C_{\infty}}-algebras whose cohomology algebras are those of{(S^{p}\times S^{p+2q-1})\sharp(S^{q}\times S^{2p+q-1})}, where{2\leq p\leq q}. We also include a proof of the decomposition theorem for cyclic{A_{\infty}}and{C_{\infty}}-algebras.

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V. Pandichelvi and B. Umamaheswari. "ERCEIVING SOLUTIONS FOR AN EXPONENTIAL DIOPHANTINE EQUATION LINKING SAFE AND SOPHIE GERMAIN PRIMES qx + py= z2." jnanabha 52, no. 02 (2022): 165–67. http://dx.doi.org/10.58250/jnanabha.2022.52219.

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In this article, an exponential Diophantine equation qx + py= z2 where p , q are Safe primes and q Sophie Germain primes respectively and x, y, z are positive integers is measured for all the opportunities of x+y = 0, 1, 2, 3 and showed that all conceivable integer solutions are (p, q, x, y, z) = (7, 3, 1, 0, 2), (11, 5, 1, 1, 4), (5, 2, 3, 0, 3), (2q + 1, q, 2, 1, q + 1) by retaining basic rules of Mathematics.

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KLYUEV, ALEXEY V., EVGENY I. SHMELEV, and ARKADY V. YAKIMOV. "MODIFICATION OF VAN DER ZIEL RELATION FOR SPECTRUM OF NOISE IN p–n JUNCTION." Fluctuation and Noise Letters 11, no. 02 (June 2012): 1250015. http://dx.doi.org/10.1142/s0219477512500150.

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Spectrum SiD of the white current noise iD(t) in p–n junction with the ideality factor η of the current–voltage characteristic, which is greater than one, is investigated here. It is shown, that the Van der Ziel relation, SiD = 2q(ID + 2Is), intended for η = 1, is inapplicable if η > 1; here q is the elementary charge, ID is the current through the junction, and Is is the saturation current. As the first step, the simplest case is considered, η = 2. That is the main recombination of injected electrons and holes takes place in the middle of the junction depleted region. Such junction may be modeled by two identical junctions with η = 1, which are connected in series. The current noise iD(t) is determined by noise sources of both junctions. Obtained result is generalized by the use of the Gupta theorem for the thermal noise spectrum in nonlinear resistive systems. The current noise spectrum is found, SiD = (2q/η) · (ID + 2Is). This result is the modification of the Van der Ziel relation extended to η ≥ 1. Experimental proof of the modified relation is made by analysis of the white noise spectrum in Schottky diode with δ-doping (having η = 2.2) in the vicinity of thermodynamical equilibrium.

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Park, Young-Taek, JeongYun Park, Ji Soo Jeon, Young Jae Kim, and Kwang Gi Kim. "Changes in Nurse Staffing Grades of Korean Hospitals during COVID-19 Pandemic." International Journal of Environmental Research and Public Health 18, no. 11 (May 31, 2021): 5900. http://dx.doi.org/10.3390/ijerph18115900.

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The global COVID-19 pandemic is creating challenges to manage staff ratios in clinical units. Nurse staffing level is an important indicator of the quality of care. This study aimed to identify any changes in the nurse staffing levels in the general wards of hospitals in Korea during the COVID-19 pandemic. The unit of analysis was the hospitals. This longitudinal study observed the quarterly change of the nurse staffing grades in 969 hospitals in 2020. The nurse staffing grades ranged from 1 to 7 according to the nurse–patient ratio measured by the number of patients (or beds) per nurse. The major dependent and independent variables were the change of nurse staffing grades and three quarterly observation points being compared with those during the 1st quarter (1Q) of 2020, respectively. A generalized linear model was used. Unexpectedly, the nurse staffing grades significantly improved (2Q: RR, 27.2%; 95% confidence interval (CI), 15.1–27.6; p < 0.001; 3Q: RR, 95% CI, 20.2%; 16.9–21.6; p < 0.001; 4Q: RR, 26.6%; 95% CI, 17.8–39.6; p < 0.001) quarterly, indicating that the nurse staffing levels increased. In the comparison of grades at 2Q, 3Q, and 4Q with those at 1Q, most figures improved in tertiary, general, and small hospitals (p < 0.05), except at 3Q and 4Q of general hospitals. In conclusion, the nurse staffing levels did not decrease, but nursing shortage might occur.

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Shirai, M., M. S. Vacchio, R. J. Hodes, and J. A. Berzofsky. "Preferential V beta usage by cytotoxic T cells cross-reactive between two epitopes of HIV-1 gp160 and degenerate in class I MHC restriction." Journal of Immunology 151, no. 4 (August 15, 1993): 2283–95. http://dx.doi.org/10.4049/jimmunol.151.4.2283.

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Abstract The T cell response to HIV-1 gp160 is among the most thoroughly studied immune responses to HIV-1 products. In our previous work, the MHC class I molecule Dd as well as H-2u, p, and q, were found to present P18 and HP53, two determinants of HIV-1 gp160, to CD8+ CTL in mice. We have studied the TCR V beta chain expression in CTL lines, either cross-reactive for these two peptides or specific for P18 alone, in these four different MHC haplotypes. The usage of V beta in T cells showing cross-reaction between these two peptides was remarkably conserved (primarily V beta 8 family, with some use of V beta 14) despite the extensive TCR V beta diversity of the non-cross-reactive CTL, which did not use V beta 8 or 14. This correlation of V beta usage with fine specificity was consistent in H-2d, u, and p (p < 0.01), but not in H-2q. The correlation of V beta use with peptide fine specificity independent of MHC restriction was unexpected. The strong predominance of V beta 8 family TCR was all the more surprising in view of the finding that mice bearing a genomic deletion of V beta 8 can still produce T cells with the cross-reactive phenotype, implying that other V beta chains can produce this specificity. We therefore asked whether the complexes of P18 with H-2d, p, and u are recognized as identical, and observed the surprising result that H-2d, p, and u cells mutually cross-present the peptides P18 and HP53 to allogeneic CTL lines and individual clones of each of the other haplotypes, whereas none of these cross-present to H-2q CTL, nor do H-2q targets present to CTL of the other haplotypes. This degeneracy of MHC restriction is novel for class I molecules. Moreover, the observed restriction in V beta usage occurs only in the unique set of CTL that exhibit both peptide-cross-reactive fine specificity and MHC allogeneic cross-presentation. The observation that a strain of mice in which the V beta 8 family is genomically deleted can still make CTL of this phenotype using another V beta demonstrates the plasticity of the class I MHC-restricted repertoire when the dominating receptor is not available.

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32

Boyde, Guy. "Bounding size of homotopy groups of Spheres." Proceedings of the Edinburgh Mathematical Society 63, no. 4 (November 2020): 1100–1105. http://dx.doi.org/10.1017/s001309152000036x.

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AbstractLet p be prime. We prove that, for n odd, the p-torsion part of πq(Sn) has cardinality at most $p^{2^{{1}/({p-1})(q-n+3-2p)}}$ and hence has rank at most 21/(p−1)(q−n+3−2p). for p = 2, these results also hold for n even. The best bounds proven in the existing literature are $p^{2^{q-n+1}}$ and 2q−n+1, respectively, both due to Hans–Werner Henn. The main point of our result is therefore that the bound grows more slowly for larger primes. As a corollary of work of Henn, we obtain a similar result for the homotopy groups of a broader class of spaces.

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IKEDA, TORU. "BOUNDARIES OF INCOMPRESSIBLE SURFACES IN GRAPH KNOT EXTERIORS." Journal of Knot Theory and Its Ramifications 19, no. 01 (January 2010): 71–79. http://dx.doi.org/10.1142/s0218216510007747.

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We will study boundaries of incompressible surfaces properly embedded in graph knot exteriors. We will first show that any bounded two-sided surface is meridional or longitudinal. In particular, iterated torus knot exteriors contain no bounded two-sided essential surface which is meridional or preferred longitudinal but Seifert surfaces. Even if the surface is possibly one-sided, the boundary is not of type (2p, 2q + 1) for any integers p and q.

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Zhelezov, Ognyan Ivanov, and Valentina Markova Petrova. "Application of the Transpositions matrix for obtaining n-dimensional rotation matrices." International Journal of Chemistry, Mathematics and Physics 6, no. 5 (2022): 12–18. http://dx.doi.org/10.22161/ijcmp.6.5.3.

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This article proposes an algorithm for generation of N-dimensional rotation matrix R, N=m+n, m=2p, n=2q, p,q  [2, 4, 8] which rotates given N-dimensional vector X in the direction of coordinate axis x1 Algorithm uses block diagonal matrix, composed by Transpositions matrices. As practical realization article gives Matlab code of functions, which creates Householder and Transpositions matrices and V matrix for given n-dimensional vector X.

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35

Dholey, S. "Effect of Magnetic Field on the Unsteady Boundary Layer Flows Induced by an Impulsive Motion of a Plane Surface." Zeitschrift für Naturforschung A 75, no. 4 (April 28, 2020): 343–55. http://dx.doi.org/10.1515/zna-2019-0334.

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AbstractThe unsteady laminar boundary layer flow of an electrically conducting viscous fluid near an impulsively started flat plate of infinite extent is considered, with a view to examine the influence of transverse magnetic field fixed to the fluid. A new type of similarity transformation is proposed, which renews the governing partial differential equation into a linear ordinary differential equation with four physical parameters, viz. unsteadiness parameter β, magnetic parameter M, and the velocity indices (p, q). The analytic solution of this equation has been found in terms of a first kind confluent hypergeometric function for some specific parameter regimes. This solution shows the structure of a new type of boundary layer flow that includes the solution of the first Stokes problem as a special case. For non-zero values of (p, q), there is a definite range of p (either −∞ < p < 2q or 2q < p < ∞ according to β < or > 0) for which this flow problem will be valid. This analysis reveals an important relation $(p\beta+{M^{2}}=q\beta)$ at which separation appears inside the layer and has been detected as the separation threshold of the problem. Indeed, this relation gives us the critical value of one when the others are known. Flow separation inside the layer is delayed with an increasing value of q but cannot be completely removed whatever is the value of q (>0). The present analysis ensures that the reverse flow can be suppressed by the use of a proper amount of magnetic field M depending upon the values of p, q, and β. The obtained result provides insight into the stability of the boundary layer flows.

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36

Shirai, M., S. Kozlowski, D. H. Margulies, and J. A. Berzofsky. "Degenerate MHC restriction reveals the contribution of class I MHC molecules in determining the fine specificity of CTL recognition of an immunodominant determinant of HIV-1 gp160 V3 loop." Journal of Immunology 158, no. 7 (April 1, 1997): 3181–88. http://dx.doi.org/10.4049/jimmunol.158.7.3181.

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Abstract The novel allogeneic presentation of an immunodominant determinant within the HIV-1 gp160 V3 loop by three different class I MHC molecules to the same CD8+ CTL is used to study the influence of the MHC molecule on the fine specificity of CTL recognition. We previously reported that four distinct class I molecules of H-2d,u,p,q presented the V3 decapeptide P18-I10 (RGPGRAFVTI) to CTL. Surprisingly, we found that H-2d,u,p cells mutually cross-present the P18-I10 peptide to allogeneic CTL clones of each of the other haplotypes, whereas none of these cross-presents to H-2q CTL, nor do H-2q targets present to CTL of the other haplotypes. Here, we explore the critical amino acid residues for the cross-presentation using 10 variant peptides with single amino acid substitutions. The fine specificity examined using these mutant peptides presented by the same MHC class I molecule showed striking similarity among the CTL of each haplotype, expressing either V beta 8.1 or V beta 14. In contrast, the fine specificity is different between the distinct MHC class I molecules even for the lysis by the same CTL, as shown by reciprocal effects of the same substitutions. Thus, peptide fine specificity of a single TCR is influenced by changes in the class I MHC molecules presenting the Ag.

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MUKOYAMA, Kazuo. "SMOOTH SU (p,q)-ACTIONS ON THE (2p+2q-1)-SPHERE AND ON THE COMPLEX PROJECTIVE (p+q-1)-SPACE." Kyushu Journal of Mathematics 55, no. 2 (2001): 213–36. http://dx.doi.org/10.2206/kyushujm.55.213.

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38

Qi, Lan, and Xiaoxue Li. "The Diophantine Equation8x+py=z2." Scientific World Journal 2015 (2015): 1–3. http://dx.doi.org/10.1155/2015/306590.

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Letpbe a fixed odd prime. Using certain results of exponential Diophantine equations, we prove that (i) ifp≡±3(mod 8), then the equation8x+py=z2has no positive integer solutions(x,y,z); (ii) ifp≡7(mod 8), then the equation has only the solutions(p,x,y,z)=(2q-1,(1/3)(q+2),2,2q+1), whereqis an odd prime withq≡1(mod 3); (iii) ifp≡1(mod 8)andp≠17, then the equation has at most two positive integer solutions(x,y,z).

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39

Diego, V. P., L. Almasy, D. L. Rainwater, M. C. Mahaney, A. G. Comuzzie, S. A. Cole, R. P. Tracy, M. P. Stern, J. W. MacCluer, and J. Blangero. "A Quantitative Trait Locus on Chromosome 5p Influences D-Dimer Levels in the San Antonio Family Heart Study." International Journal of Vascular Medicine 2010 (2010): 1–6. http://dx.doi.org/10.1155/2010/490241.

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Background. D-dimer is associated with increasing severity of atherosclerosis and with increased risk of a cardiovascular disease (CVD).Methods and Results. To better understand this risk factor, we performed a genome scan on 803 (301 males and 502 females) Mexican Americans in the San Antonio Family Heart Study (SAFHS). The SAFHS is ideal for the discovery of quantitative trait loci (QTLs) influencing CVD because CVD risk factors are prevalent in Mexican Americans of San Antonio and because the study design involves large families, which is optimal for QTL discovery. D-dimer levels were normalized in our study. We found that D-dimer levels were heritable, at about 23% heritability (P≈.00001). In a linkage analysis employing 432 microsatellite markers, we found strong evidence of a QTL on chromosome 5p with a lod score of 3.32 at 21 centiMorgans (cM). We also found suggestive evidence of a QTL on chromosome 2q with a lod score of 2.33 at 207 cM.Conclusions. To our knowledge, the putative QTL on chromosome 5p is novel. The possible QTL on chromosome 2q is discussed in relation to a recent report of linkage of a related hemostatic factor to the same location. These results warrant further investigation.

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Kroll, Hans-Joachim, and Rita Vincenti. "(2q+1)-Arcs in PG(3,q^3) stabilized by a p-Sylow of PSL(2,q)." International Mathematical Forum 8 (2013): 727–42. http://dx.doi.org/10.12988/imf.2013.13077.

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41

Nurhakim, Rusdan. "An Odd-Even Sum Labeling of Jellyfish and Mushroom Graphs." InPrime: Indonesian Journal of Pure and Applied Mathematics 2, no. 2 (June 7, 2020): 87–90. http://dx.doi.org/10.15408/inprime.v2i2.14620.

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AbstractA graph G(V,E) with p vertices and q edges called graph odd-even sum if there exists an injective function f from V to {+ 1, +2, +3, ..., +(2p-1)} such that induced a bijection f*(uv)=f(u)+f(v) as label of edge and u,v element of V forms the set {2,4,...,2q}, and f is called odd-even sum labeling. There are three criteria of graphs that can be labeled by this labeling, they are undirected, no loops, and finite for every edges and vertex. Jellyfish J(m,n) graph and Mushroom Mr(m) graph have the criteria. So in this paper will be showed that the Jellyfish and Mushroom graphs can be labeled by this labeling.Keywords: odd-even sum graph; odd-even sum labeling; Jellyfish and mushroom graphs. AbstrakGraf G(V,E) dengan banyak titik p dan sisi q dikatakan graf jumlah ganjil-genap jika terdapat suatu fungsi injetif f dari V ke {+ 1, +2, +3, ..., +(2p-1)} sehingga bijektif f*(uv)=f(u)+f(v) merupakan label sisi dengan u,v anggota dari V membentuk himpunan bilangan {2,4,...,2q}, dengan f merupakan pelabelan jumlah ganjil-genap. Kriteria graf yang dapat dilabeli oleh pelabelan jumlah ganjil-genap ada tiga, yaitu graf yang tidak berarah, tidak memiliki loop, dan terhingga, baik secara sisi maupun titik. Graf Jellyfish J(m,n) dan Mushroom Mr(m) memenuhi ketiga kriteria tersebut. Pada tulisan ini akan ditunjukkan bahwa kedua graf tersebut dapat dilabeli dengan pelabelan jumlah ganjil-genap.Keywords: graf jumlah ganjil-genap; pelabelan jumlah ganjil-genap; graf Jellyfish dan graf Mushroom.

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42

KIM, DAE-YEOUL, JA-KYUNG KOO, and MYUNG-HWAN KIM. "CONGRUENCE EQUATIONS OF axi+ byj≡ c AND axi+ byj+ dzt≡ c(modp) WHEN p=2q+1 WITH p AND q ODD PRIMES." Communications of the Korean Mathematical Society 20, no. 3 (July 1, 2005): 467–85. http://dx.doi.org/10.4134/ckms.2005.20.3.467.

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43

Fujiwara, Shin-ichiro, Yoshihiro Yamashita, Naoya Nakamura, Masafumi Abe, Keiya Ozawa, and Hiroyuki Mano. "Outcome-Related Genome Loci in T-Cell Non-Hodgkin’s Lymphoma Identified by High-Resolution SNP-Typing Arrays." Blood 108, no. 11 (November 1, 2006): 2056. http://dx.doi.org/10.1182/blood.v108.11.2056.2056.

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Abstract Peripheral T-cell lymphoma, unspecified (PTCL) and angioimmunoblastic T-cell lymphoma (AITL) are non-Hodgkin’s lymphoma of T-cell origin. Despite their relatively poor outcome, little is yet understood for the molecular pathogenesis of these disorders. To screen for transforming/tumor-suppressor genes among PTCL/AITL, we here tried to examine copy number alterations (CNAs) among HTLV-I-negative lymph node specimens of PTCL (n = 32) and AITL (n = 42). Utilization of high-density SNP-typing arrays (GeneChip Mapping 100K Hind III, Affymetrix) has allowed us to measure CNA at a mean resolution of 47 kbp among the samples. Interestingly, both of PTCL and AITL cells have frequent CNAs throughout the genome. Among the 55,700 SNP sites examined for PTCL, for instance, chromosome copy number at 20,860 sites was shown to be ≥ 3 in at least 2 specimens, while loss of copy number (≤ 1) was found at 2,287 sites in ≥ 2 samples. Similarly, among the AITL specimens, copy number gain (≥ 3) in ≥ 2 samples was observed at 9,897 SNP sites, and copy number loss in ≥ 2 samples was identified at 43 sites. We further searched for frequent CNAs among the whole dataset, revealing that copy number gain of ≥ 4 was observed in ≥ 10 cases at 1q, 2p, 2q, 8q, 9p, 13q, 15q, and 19q. On the other hand, copy number of ≤ 1 was found among ≥ 10 cases at 14q. Further, the copy number of a genomic region was shown to be linked to a differential diagnosis of PTCL/AITL. From the same dataset, we could also reveal a vast number of loss-of-heterozygosity (LOH) regions with a divergent length. Frequent LOH (≥ 5 cases) was mapped to 2q, 5q, 8p and 9p. By using a Cox proportional hazard analysis, we then investigated whether chromosome copy number or LOH likelihood is statistically linked to prognosis of the patients enrolled in this study. Interestingly, the copy number of narrow regions at 2q, 5p, 5q and 17q was shown to be statistically associated with the clinical outcome (P <0.01) while the LOH-likelihood at 8q was linked to it (P <0.05). The chromosomal regions identified in our screening are the good candidates where transforming- or/and clinical character-related genes are mapped. Especially, the narrow regions thus identified contain a few genes per region, and provide us with a provocative list of PTCL/AITL-related genes.

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44

Purohit, G. N., Usha Sharma, and Rinku Chaudhary. "Odd Graceful Labeling Of Tensor Product of Some Graphs." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 10, no. 7 (August 30, 2013): 1825–29. http://dx.doi.org/10.24297/ijct.v10i7.3213.

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(G);E(G)) with p vertices and q edges, if there exists an injectionfunction : V (G) ! f0; 1; 2; ; 2q ô€€€ 1g with each edge uv assignedthe label jf(u)ô€€€f(v)j, the resulting edge labels are f1; 3; 5; ; 2qô€€€1g.The tensor product of two graphs, G and H, has a vertex setV (G) V (H) and an edge between (u; v) and (u0; v0), i both uu0 2 E(G) andvv0 2 E(H), here we denote tensor product by ^. In this paper, weprove Sn ^ Sm, Sn ^ Pm and Cn ^ Sm are odd graceful.

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45

Abreu Blaya, Ricardo, Juan Bory Reyes, Richard Delanghe, and Frank Sommen. "Generalized Moisil-Théodoresco Systems and Cauchy Integral Decompositions." International Journal of Mathematics and Mathematical Sciences 2008 (2008): 1–19. http://dx.doi.org/10.1155/2008/746946.

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Letℝ0,m+1(s)be the space ofs-vectors(0≤s≤m+1)in the Clifford algebraℝ0,m+1constructed over the quadratic vector spaceℝ0,m+1, letr,p,q∈ℕwith0≤r≤m+1, 0≤p≤q, andr+2q≤m+1, and letℝ0,m+1(r,p,q)=∑j=pq⨁ ℝ0,m+1(r+2j). Then, anℝ0,m+1(r,p,q)-valued smooth functionWdefined in an open subsetΩ⊂ℝm+1is said to satisfy the generalized Moisil-Théodoresco system of type(r,p,q)if∂xW=0inΩ, where∂xis the Dirac operator inℝm+1. A structure theorem is proved for such functions, based on the construction of conjugate harmonic pairs. Furthermore, ifΩis bounded with boundaryΓ, whereΓis an Ahlfors-David regular surface, and ifWis aℝ0,m+1(r,p,q)-valued Hölder continuous function onΓ, then necessary and sufficient conditions are given under whichWadmits onΓa Cauchy integral decompositionW=W++W−.

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46

YEN, CHEN-TE. "ON A THEOREM OF HERSTEIN." Tamkang Journal of Mathematics 21, no. 2 (June 1, 1990): 123–30. http://dx.doi.org/10.5556/j.tkjm.21.1990.4646.

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Let $R$ be an associative ring with identity such that for some fixed integer $m >1$, $(x+y)^m =x^m+y^m$ for all $x,y$ in $R$. If $m =2$ (mod 4) ,or $p-1|m-1$ for each prime factor $p$ of $m$, then $R$ is commutative. The restriction on $m$ is essential. Moreover, in case of $m=2$ (mod 4) and $m >2$, then $R$ is isomorphic to a subdirect sum of subdirectly irreducible rings $R_i$ each of which, as homomorphic images of $R$, satisfies the same polynomial identity $(x +y)^m =x^m +y^m$; and for each $x$ in $R_i$;,either $x^2 =0$ or $x^{2q} =1$, where $(q,m)=1$.

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47

Bagderina, Yu Yu. "Equivalence of ordinary differential equations y″ = R(x, y)y′ 2 + 2Q(x, y)y′ + P(x, y)." Differential Equations 43, no. 5 (May 2007): 595–604. http://dx.doi.org/10.1134/s0012266107050035.

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48

Lee, Rachael A., Jeremey Walker, Elizabeth Freeze, Rashida Khalid, and Bernard Camins. "2353. Easy Does It: Decreasing and Sustained Hospital-Onset (HO) CDI Lab-ID Event Incidence Through a Series of Interventions." Open Forum Infectious Diseases 6, Supplement_2 (October 2019): S809—S810. http://dx.doi.org/10.1093/ofid/ofz360.2031.

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Abstract Background Clostridioides difficile infection (CDI) Laboratory (Lab) identified (ID) events are reportable to CMS through the CDC’s NHSN. Prevention of transmission has been the main component of interventions; however, avoiding false-positive laboratory diagnoses can also lead to decreased incidence. Methods A retrospective analysis of HO-CDI Lab-ID events was conducted to evaluate the results of a series of interventions at the University of Alabama Hospital, a 1150-bed tertiary care center in Birmingham, AL. The study period was from the first quarter of 2013 (1Q 2013) until 1Q of 2019. Interventions were implemented in sequential order were: (i) CDI prevention bundle education (3Q 2014); (ii) two-step laboratory testing algorithm (2Q 2015); (iii) selective enhanced environmental disinfection on oncology units (2Q 2016); (iv) diagnostic stewardship by reminding providers to reconsider testing if the patient received a laxative within 48 hours (4Q 2016). Results At the beginning of the study period, the HO CDI Lab ID Event SIR was 0.96. The standard infection ratio (SIR) over the time period is shown in Figure 1. We observed a slight decrease in HO-CDI Lab ID event SIR after implementation of the CDI prevention bundle (0.96 vs. 0.77). A change in the diagnostic testing from PCR-based to a two-step algorithm (EIA testing for GDH and Toxin confirmed by PCR) resulted in a slight increase although not statistically significant (0.77 vs. 0.83). A downward trend was observed when selective enhanced terminal disinfection with hydrogen peroxide vapor was performed on all oncology patient rooms vacated by patients with CDI (0.83 vs. 0.72). The largest and sustained impact was observed after implementation of a computer-assisted diagnostic stewardship in which providers were reminded if the patient was administered any stool softener or laxative within 48 hours of the order for CDI testing (0.72 vs. 0.32). The institutions SIR value became significant in 2Q 2016 (P = 0.0014) and significance was maintained since that time. The difference between expected and observe HO-CDI Lab ID events is demonstrated in Figure 2. Conclusion Through a series of interventions, we observed a decrease in HO-CDI event rates. Diagnostic stewardship with academic detailing resulted in the most impactful and sustained improvement. Disclosures All authors: No reported disclosures.

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JORRAND, PHILIPPE, and MEHDI MHALLA. "SEPARABILITY OF PURE N-QUBIT STATES: TWO CHARACTERIZATIONS." International Journal of Foundations of Computer Science 14, no. 05 (October 2003): 797–814. http://dx.doi.org/10.1142/s0129054103002035.

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Given a pure state |ψN>∈ℋN of a quantum system composed of n qubits, where ℋN is the Hilbert space of dimension N=2n, this paper answers two questions: what conditions should the amplitudes in |ψN> satisfy for this state to be separable (i) into a tensor product of n qubit states |ψ2>0⊗ |ψ2>1 ⊗⋯⊗ |ψ2>n-1, and (ii), into a tensor product of two subsystems states |ψP> ⊗ |ψQ> with P=2p and Q=2q such that p+q=n? For both questions, necessary and sufficient conditions are proved, thus characterizing at the same time families of separable and entangled states of n qubit systems. A number of more refined questions about separability in n qubit systems can be studied on the basis of these results.

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50

Wang, Caixia, Liangxin Fan, Zhenliang Pan, Sufang Fan, Lijun Shi, Xu Li, Jinfang Zhao, Lulu Wu, Guoyu Yang, and Cuilian Xu. "Synthesis of Novel Indole Schiff Base Compounds and Their Antifungal Activities." Molecules 27, no. 20 (October 13, 2022): 6858. http://dx.doi.org/10.3390/molecules27206858.

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A series of novel indole Schiff base derivatives (2a–2t) containing a 1,3,4-thiadiazole scaffold modified with a thioether group were synthesized, and their structures were confirmed using FT-IR, 1H NMR, 13C NMR, and HR-MS. In addition, the antifungal activity of synthesized indole derivatives was investigated against Fusarium graminearum (F. graminearum), Fusarium oxysporum (F. oxysporum), Fusariummoniliforme (F.moniliforme), Curvularia lunata (C. lunata), and Phytophthora parasitica var. nicotiana (P. p. var. nicotianae) using the mycelium growth rate method. Among the synthesized indole derivatives, compound 2j showed the highest inhibition rates of 100%, 95.7%, 89%, and 76.5% at a concentration of 500 μg/mL against F. graminearum, F. oxysporum, F.moniliforme, and P. p. var. nicotianae, respectively. Similarly, compounds 2j and 2q exhibited higher inhibition rates of 81.9% and 83.7% at a concentration of 500 μg/mL against C. lunata. In addition, compound 2j has been recognized as a potential compound for further investigation in the field of fungicides.

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