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Journal articles on the topic 'Q-Analogs'

Author: Grafiati

Published: 11 January 2025

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1

Al-Omari, Shrideh, Wael Salameh, and Hamzeh Zureigat. "Convolution Theorem for p,q-Gamma Integral Transforms and Their Application to Some Special Functions." Symmetry 16, no. 7 (July 11, 2024): 882. http://dx.doi.org/10.3390/sym16070882.

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This article introduces (p,q)-analogs of the gamma integral operator and discusses their expansion to power functions, (p,q)-exponential functions, and (p,q)-trigonometric functions. Additionally, it validates other findings concerning (p,q)-analogs of the gamma integrals to unit step functions as well as first- and second-order (p,q)-differential operators. In addition, it presents a pair of (p,q)-convolution products for the specified (p,q)-analogs and establishes two (p,q)-convolution theorems.

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2

Sagan, Bruce E. "Congruence properties of q-analogs." Advances in Mathematics 95, no. 1 (September 1992): 127–43. http://dx.doi.org/10.1016/0001-8708(92)90046-n.

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3

Braun, Michael, and Jan Reichelt. "q-Analogs of Packing Designs." Journal of Combinatorial Designs 22, no. 7 (October 15, 2013): 306–21. http://dx.doi.org/10.1002/jcd.21376.

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4

Al-Omari, Shrideh, and Wael Salameh. "On (p,q)-Analogs of the α-th Fractional Fourier Transform and Some (p,q)-Generalized Spaces." Symmetry 16, no. 10 (October 3, 2024): 1307. http://dx.doi.org/10.3390/sym16101307.

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In this article, the (p,q)-analogs of the α-th fractional Fourier transform are provided, along with a discussion of their characteristics in specific classes of (p,q)-generalized functions. Two spaces of infinitely (p,q)-differentiable functions are defined by introducing two (p,q)-differential symmetric operators. The (p,q)-analogs of the α-th fractional Fourier transform are demonstrated to be continuous and linear between the spaces under discussion. Next, theorems pertaining to specific convolutions are established. This leads to the establishment of multiple symmetric identities, which in turn requires the construction of (p,q)-generalized spaces known as (p,q)-Boehmians. Finally, in addition to deriving the inversion formulas, the generalized (p,q)- analogs of the α-th fractional Fourier transform are introduced, and their general properties are discussed.

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5

Zabrocki, Michael. "q-Analogs of symmetric function operators." Discrete Mathematics 256, no. 3 (October 2002): 831–53. http://dx.doi.org/10.1016/s0012-365x(02)00350-3.

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6

Ivanov, V. N. "Interpolation Analogs of Schur Q-Functions." Journal of Mathematical Sciences 131, no. 2 (November 2005): 5495–507. http://dx.doi.org/10.1007/s10958-005-0422-6.

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7

Bergeron, Nantel, and Michael Zabrocki. "q and q,t-analogs of non-commutative symmetric functions." Discrete Mathematics 298, no. 1-3 (August 2005): 79–103. http://dx.doi.org/10.1016/j.disc.2004.08.044.

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8

Al-Omari, Shrideh, Wael Salameh, and Sharifah Alhazmi. "Some Estimates for Certain q-analogs of Gamma Integral Transform Operators." Symmetry 16, no. 10 (October 15, 2024): 1368. http://dx.doi.org/10.3390/sym16101368.

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The aim of this work is to examine some q-analogs and differential properties of the gamma integral operator and its convolution products. The q-gamma integral operator is introduced in two versions in order to derive pertinent conclusions regarding the q-exponential functions. Also, new findings on the q-trigonometric, q-sine, and q-cosine functions are extracted. In addition, novel results for first and second-order q-differential operators are established and extended to Heaviside unit step functions. Lastly, three crucial convolution products and extensive convolution theorems for the q-analogs are also provided.

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9

Alsoboh, Abdullah, Ala Amourah, Maslina Darus, and Carla Amoi Rudder. "Studying the Harmonic Functions Associated with Quantum Calculus." Mathematics 11, no. 10 (May 9, 2023): 2220. http://dx.doi.org/10.3390/math11102220.

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Using the derivative operators’ q-analogs values, a wide variety of holomorphic function subclasses, q-starlike, and q-convex functions have been researched and examined. With the aid of fundamental ideas from the theory of q-calculus operators, we describe new q-operators of harmonic function Hϱ,χ;qγF(ϖ) in this work. We also define a new harmonic function subclass related to the Janowski and q-analog of Le Roy-type functions Mittag–Leffler functions. Several important properties are assigned to the new class, including necessary and sufficient conditions, the covering Theorem, extreme points, distortion bounds, convolution, and convex combinations. Furthermore, we emphasize several established remarks for confirming our primary findings presented in this study, as well as some applications of this study in the form of specific outcomes and corollaries.

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10

Zhou, Xia, Tianxin Cai, and David M. Bradley. "Signed $q$-analogs of Tornheim's double series." Proceedings of the American Mathematical Society 136, no. 08 (April 8, 2008): 2689–98. http://dx.doi.org/10.1090/s0002-9939-08-09208-3.

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11

Obol'nikova, E. A., and A. I. Kozhukhova. "Biological activity of coenzyme Q analogs (review)." Pharmaceutical Chemistry Journal 27, no. 12 (December 1993): 826–33. http://dx.doi.org/10.1007/bf00780572.

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12

ADAM, DAVID. "ABEL ARITHMETIC FUNCTIONS IN FINITE CHARACTERISTIC." International Journal of Number Theory 08, no. 06 (August 3, 2012): 1557–68. http://dx.doi.org/10.1142/s1793042112500959.

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We define Abel arithmetic functions in function fields with positive characteristic. We prove that any Abel arithmetic function with exponential type lesser than [Formula: see text] is a polynomial, the bound [Formula: see text] being optimal. This provides an analog of a Bertrandias' result. Some q-analogs are considered too.

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13

Braun, Michael. "$$q$$ q -Analogs of $$t$$ t -wise balanced designs from Borel subgroups." Designs, Codes and Cryptography 78, no. 2 (September 6, 2014): 383–90. http://dx.doi.org/10.1007/s10623-014-0002-1.

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14

Gaetz, Christian, and Yibo Gao. "On q-analogs of descent and peak polynomials." European Journal of Combinatorics 97 (October 2021): 103397. http://dx.doi.org/10.1016/j.ejc.2021.103397.

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15

Sivasubramanian, Sivaramakrishnan. "q-Analogs of distance matrices of 3-hypertrees." Linear Algebra and its Applications 431, no. 8 (September 2009): 1234–48. http://dx.doi.org/10.1016/j.laa.2009.04.020.

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16

Kirkman, Ellen E., and Lance W. Small. "q-analogs of harmonic oscillators and related rings." Israel Journal of Mathematics 81, no. 1-2 (February 1993): 111–27. http://dx.doi.org/10.1007/bf02761300.

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17

Tauraso, Roberto. "q-Analogs of some congruences involving Catalan numbers." Advances in Applied Mathematics 48, no. 5 (May 2012): 603–14. http://dx.doi.org/10.1016/j.aam.2011.12.002.

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18

Guan, Hao, Sibel Koparal, Neşe Ömür, and Waseem Ahmad Khan. "q-Analogs of Hn,mrσ and Their Applications." Mathematics 11, no. 19 (October 3, 2023): 4159. http://dx.doi.org/10.3390/math11194159.

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19

Khare, Chandrashekhar, and Niccoló Ronchetti. "Derived Hecke action at p and the ordinary p -adic cohomology of arithmetic manifolds." American Journal of Mathematics 145, no. 6 (December 2023): 1631–94. http://dx.doi.org/10.1353/ajm.2023.a913294.

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Abstract: We study the derived Hecke action at $p$ on the ordinary $p$-adic cohomology of arithmetic subgroups of reductive groups ${\rm G}(\Bbb{Q})$. This is the analog at $\ell=p$ of derived Hecke actions studied by Venkatesh in the tame case, and is the derived analog of Hida's theory for ordinary Hecke algebras. We show that properties of the derived Hecke action at $p$ are related to deep conjectures in Galois cohomology which are higher analogs of the classical Leopoldt conjecture.

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20

Smirnov, Yu F., and Yu I. Kharitonov. "Quantum algebra U q(2, 1): q analogs of the Gelfand-Graev formulas." Physics of Atomic Nuclei 64, no. 12 (December 2001): 2167–72. http://dx.doi.org/10.1134/1.1432920.

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21

Kruse, V., I. Jensen, L. Permin, and A. Heding. "Fate of insulin analogs in intact and nephrectomized rats determined by their receptor binding constants." American Journal of Physiology-Endocrinology and Metabolism 272, no. 6 (June 1, 1997): E1089—E1098. http://dx.doi.org/10.1152/ajpendo.1997.272.6.e1089.

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After intravenous injection of 125I-labeled human insulin and analogs in normal and nephrectomized rats, we examined their kinetic fate by Q-Sepharose separation into intact ligand, "fragments" (genuine fragments and protein-bound radioactivity), and iodide. Receptor binding association and dissociation constants (kass and kdis, respectively) of the analogs were estimated dynamically in vitro by BIAcore. The very fast disappearance of intact ligand from serum was found to be determined by 1) both kass and kdis of receptor-bearing tissue, thus substantiating our primary hypothesis; 2) elimination by kidneys, and 3) fast extravascularization. The rate of appearance of degradation products from receptor-mediated intracellular processing seems determined by kdis. With the possible exception of a truncated analog, ligand appears protected against degradation while the intracellular receptor-ligand complex remains intact. Non-receptor-mediated processing in kidneys is slow, compared with the receptor-mediated uptake and degradation of ligands with rate constants comparable to those of insulin. We observed binding of insulin and analogs putatively to serum proteins; binding capacity and affinity appeared insignificant for insulin but considerable for some analogs.

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22

Tauraso, Roberto. "Some q-analogs of congruences for central binomial sums." Colloquium Mathematicum 133, no. 1 (2013): 133–43. http://dx.doi.org/10.4064/cm133-1-9.

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23

Vardy, Alexander, and Tuvi Etzion. "On $q$-analogs of Steiner systems and covering designs." Advances in Mathematics of Communications 5, no. 2 (May 2011): 161–76. http://dx.doi.org/10.3934/amc.2011.5.161.

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24

Méndez, M., and A. Rodriguez. "q-analogs of the generalized Stirling and Bell numbers." Journal of Physics: Conference Series 104 (March 1, 2008): 012019. http://dx.doi.org/10.1088/1742-6596/104/1/012019.

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25

Zhou, Roberta R., and Wenchang Chu. "Identities on Extended Catalan Numbers and Their q-Analogs." Graphs and Combinatorics 32, no. 5 (April 12, 2016): 2183–97. http://dx.doi.org/10.1007/s00373-016-1694-y.

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26

Chakrabarti, A. "q‐analogs of IU(n) and U(n,1)." Journal of Mathematical Physics 32, no. 5 (May 1991): 1227–34. http://dx.doi.org/10.1063/1.529319.

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27

LIU, JI-CAI, and ZHONG-YU HUANG. "A TRUNCATED IDENTITY OF EULER AND RELATED -CONGRUENCES." Bulletin of the Australian Mathematical Society 102, no. 3 (April 8, 2020): 353–59. http://dx.doi.org/10.1017/s0004972720000301.

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We discuss a truncated identity of Euler and present a combinatorial proof of it. We also derive two finite identities as corollaries. As an application, we establish two related $q$-congruences for sums of $q$-Catalan numbers, one of which has been proved by Tauraso [‘$q$-Analogs of some congruences involving Catalan numbers’, Adv. Appl. Math. 48 (2012), 603–614] by a different method.

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28

Li, Zhi-Hua, and An-Min Wang. "Entanglement entropy in quasi-symmetric multi-qubit states." International Journal of Quantum Information 13, no. 02 (March 2015): 1550007. http://dx.doi.org/10.1142/s0219749915500070.

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We generalize the symmetric multi-qubit states to their q-analogs, whose basis vectors are identified with the q-Dicke states. We study the entanglement entropy in these states and find that entanglement is extruded towards certain regions of the system due to the inhomogeneity aroused by q-deformation. We also calculate entanglement entropy in ground states of a related q-deformed Lipkin–Meshkov–Glick (LMG) model and show that the singularities of entanglement can correctly signify the quantum phase transition points for different strengths of q-deformation.

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29

Kupershmidt, Boris A. "q-Analogs of Classical 6-Periodicity: From Euler to Chebyshev." Journal of Nonlinear Mathematical Physics 10, no. 3 (January 2003): 318–39. http://dx.doi.org/10.2991/jnmp.2003.10.3.5.

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30

Braun, Michael, Adalbert Kerber, and Reinhard Laue. "Systematic Construction of q-Analogs of t?(v,k,?)-Designs." Designs, Codes and Cryptography 34, no. 1 (January 2005): 55–70. http://dx.doi.org/10.1007/s10623-003-4194-z.

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31

Wallach, N. R., and J. Willenbring. "On Some q-Analogs of a Theorem of Kostant-Rallis." Canadian Journal of Mathematics 52, no. 2 (April 1, 2000): 438–48. http://dx.doi.org/10.4153/cjm-2000-020-0.

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AbstractIn the first part of this paper generalizationsof Hesselink’s q-analog of Kostant’smultiplicity formula for the action of a semisimple Lie group on the polynomials on its Lie algebra are given in the context of the Kostant-Rallis theorem. They correspond to the cases of real semisimple Lie groups with one conjugacy class of Cartan subgroup. In the second part of the paper a q-analog of the Kostant-Rallis theorem is given for the real group SL(4, ) (that is SO(4) acting on symmetric 4 × 4 matrices). This example plays two roles. First it contrasts with the examples of the first part. Second it has implications to the study of entanglement of mixed 2 qubit states in quantum computation.

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32

Jia, C. Z., H. M. Liu, and T. M. Wang. "q -Analogs of Generalized Fibonacci and Lucas Polynomials." Fibonacci Quarterly 45, no. 1 (February 2007): 26–34. http://dx.doi.org/10.1080/00150517.2007.12428240.

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33

Kudrevich, Svetlana V., Johan E. Van Lier, Maria G. Galpern, and Evgeny A. Luk'yanets. "Substituted tetra-2,3-pyrazinoporphyrazines. Part I. Angular annelation of tetra-2,3-quinoxalinoporphyrazine." Canadian Journal of Chemistry 74, no. 4 (April 1, 1996): 508–15. http://dx.doi.org/10.1139/v96-055.

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Several derivatives of 2,3-dicyanopyrazine were prepared via the condensation of o-quinones with diaminomaleodinitrile. Benzo[f]quinoxaline-2,3-dinitrile was obtained from 1,2-naphthoquinone, and a series of isomeric, di-tert-butyl substituted 5,6-(9,10-phenanthro)-2,3-dicyanopyrazines were prepared from the corresponding di-tert-butyl-9,10-phenanthrenequinones. Complexation of benzo[f]quinoxaline-2,3-dinitrile, and unsubstituted 5,6-(9,10-phenanthro)-2,3-dicyanopyrazine, with an appropriate metal salt yielded metal complexes of tetra-2,3-(benzo[f]quinoxalino)porphyrazine and tetra-2,3-[5,6-(9,10-phenanthro)]porphyrazine, respectively. Metal-free tetra-2,3-[5,6-(9,10-phenanthro)porphyrazine was obtained from the dilithium derivative by demetallation in HCl. These compounds have limited solubility in organic solvents, such as quinoline, and are aggregated in solutions. To eliminate the aggregation phenomenon and to determine the spectral properties of angularly annelated naphthalocyanine aza analogs, we prepared several isomeric tetra-2,3-[5,6-(di-tert-butyl-9,10-phenanthro)pyrazino]porphyrazines. These octa(tert-butyl) substituted complexes were synthesized via complexation of di-tert-butyl substituted 5,6-(9,10-phenanthro)-2,3-dicyanopyrazines with metal salts in the presence of urea, quinoline, and tri(n-butyl)amine, and purified by silica gel chromatography. They are soluble in chloroform and substantially monomerized in solutions. A hypsochromic shift of the Q-band of octaaza naphthalocyanines versus their carbocyclic analogs was observed for all aza analogs, with the extent of the shift depending on the composition of the aromatic macrocycle. Thus, the first angularly annelated benzo ring addition causes a hypsochromic shift (∼25 nm) of the Q-band of tetra-2,3-quinoxalinoporphyrazine, whereas addition of a second condensed benzo ring has little effect. Key words: phthalocyanine, aza analog, tetra-2,3-quinoxalinoporphyrazine, angular annelation.

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34

Pesini, Alba, Agustin Hidalgo-Gutierrez, and Catarina M. Quinzii. "Mechanisms and Therapeutic Effects of Benzoquinone Ring Analogs in Primary CoQ Deficiencies." Antioxidants 11, no. 4 (March 30, 2022): 665. http://dx.doi.org/10.3390/antiox11040665.

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Coenzyme Q (CoQ) is a conserved polyprenylated lipid composed of a redox-active benzoquinone ring and a long polyisoprenyl tail that serves as a membrane anchor. CoQ biosynthesis involves multiple steps, including multiple modifications of the precursor ring 4-hydroxybenzoic acid. Mutations in the enzymes involved in CoQ biosynthesis pathway result in primary coenzyme Q deficiencies, mitochondrial disorders whose clinical heterogenicity reflects the multiple biological function of CoQ. Patients with these disorders do not always respond to CoQ supplementation, and CoQ analogs have not been successful as alternative approaches. Progress made in understanding the CoQ biosynthesis pathway and studies of supplementation with 4-hydroxybenzoic acid ring analogs have opened a new area in the field of primary CoQ deficiencies treatment. Here, we will review these studies, focusing on efficacy of the different 4-hydroxybenzoic acid ring analogs, models in which they have been tested, and their mechanisms of action. Understanding how these compounds ameliorate biochemical, molecular, and/or clinical phenotypes of CoQ deficiencies is important to develop the most rational treatment for CoQ deficient patients, depending on their molecular defects.

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35

Fink, Brian D., Judith A. Herlein, Mark A. Yorek, Amanda M. Fenner, Robert J. Kerns, and William I. Sivitz. "Bioenergetic Effects of Mitochondrial-Targeted Coenzyme Q Analogs in Endothelial Cells." Journal of Pharmacology and Experimental Therapeutics 342, no. 3 (June 1, 2012): 709–19. http://dx.doi.org/10.1124/jpet.112.195586.

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36

Brylinski, Ranee-Kathryn. "Limits of Weight Spaces, Lusztig's q-Analogs, and Fiberings of Adjoint Orbits." Journal of the American Mathematical Society 2, no. 3 (July 1989): 517. http://dx.doi.org/10.2307/1990941.

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37

Nakajima, Hiraku. "Quiver varieties and t-analogs of q-characters of quantum affine algebras." Annals of Mathematics 160, no. 3 (November 1, 2004): 1057–97. http://dx.doi.org/10.4007/annals.2004.160.1057.

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38

Brylinski, Ranee Kathryn. "Limits of weight spaces, Lusztig’s $q$-analogs, and fiberings of adjoint orbits." Journal of the American Mathematical Society 2, no. 3 (September 1, 1989): 517. http://dx.doi.org/10.1090/s0894-0347-1989-0984511-x.

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39

Chen, William Y. C., and Gian-Carlo Rota. "q-Analogs of the inclusion- exclusion principle and permutations with restricted position." Discrete Mathematics 104, no. 1 (June 1992): 7–22. http://dx.doi.org/10.1016/0012-365x(92)90622-m.

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40

Andrews, George E. "q-analogs of the binomial coefficient congruences of Babbage, Wolstenholme and Glaisher." Discrete Mathematics 204, no. 1-3 (June 1999): 15–25. http://dx.doi.org/10.1016/s0012-365x(98)00364-1.

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41

Kim, Taekyun. "On the analogs of Euler numbers and polynomials associated with p-adic q-integral on Zp at q=−1." Journal of Mathematical Analysis and Applications 331, no. 2 (July 2007): 779–92. http://dx.doi.org/10.1016/j.jmaa.2006.09.027.

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42

ANANIKYAN, L. N., N. S. ANANIKIAN, and L. A. CHAKHMAKHCHYAN. "ARNOLD TONGUES AND FEIGENBAUM EXPONENTS OF THE RATIONAL MAPPING FOR Q-STATE POTTS MODEL ON RECURSIVE LATTICE: Q < 2." Fractals 18, no. 03 (September 2010): 371–83. http://dx.doi.org/10.1142/s0218348x10005007.

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We considered Q-state Potts model on Bethe lattice in presence of external magnetic field for Q < 2 by means of recursion relation technique. This allows to study the phase transition mechanism in terms of the obtained one dimensional rational mapping. The convergence of Feigenabaum α and δ exponents for the aforementioned mapping is investigated for the period doubling and three cyclic window. We regarded the Lyapunov exponent as an order parameter for the characterization of the model and discussed its dependence on temperature and magnetic field. Arnold tongues analogs with winding numbers w = 1/2, w = 2/4 and w = 1/3 (in the three cyclic window) are constructed for Q < 2. The critical temperatures of the model are discussed and their dependence on Q is investigated. We also proposed an approximate method for constructing Arnold tongues via Feigenbaum δ exponent.

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43

Bairamov, Elgiz, and Nihal Yokus. "Spectral Singularities of Sturm-Liouville Problems with Eigenvalue-Dependent Boundary Conditions." Abstract and Applied Analysis 2009 (2009): 1–8. http://dx.doi.org/10.1155/2009/289596.

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LetLdenote the operator generated inL2(R+)by Sturm-Liouville equation−y′′+q(x)y=λ2y,x∈R+=[0,∞),y′(0)/y(0)=α0+α1λ+α2λ2, whereqis a complex-valued function andαi∈ℂ,i=0,1,2withα2≠0. In this article, we investigate the eigenvalues and the spectral singularities ofLand obtain analogs of Naimark and Pavlov conditions forL.

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44

Genova, Maria Luisa, Milena Merlo Pich, Annalisa Biondi, Andrea Bernacchia, Anna Falasca, Carla Bovina, Gabriella Formiggini, Giovanna Parenti Castelli, and Giorgio Lenaz. "Mitochondrial Production of Oxygen Radical Species and the Role of Coenzyme Q as an Antioxidant." Experimental Biology and Medicine 228, no. 5 (May 2003): 506–13. http://dx.doi.org/10.1177/15353702-0322805-14.

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The mitochondrial respiratory chain is a powerful source of reactive oxygen species (ROS), which is considered as the pathogenic agent of many diseases and of aging. We have investigated the role of complex I in superoxide radical production and found by the combined use of specific inhibitors of complex I that the one-electron donor to oxygen in the complex is a redox center located prior to the sites where three different types of Coenzyme Q (CoQ) competitors bind, to be identified with an Fe–S cluster, most probably N2, or possibly an ubisemiquinone intermediate insensitive to all the above inhibitors. Short-chain Coenzyme Q analogs enhance superoxide formation, presumably by mediating electron transfer from N2 to oxygen. The clinically used CoQ analog, idebenone, is particularly effective, raising doubts on its safety as a drug. Cells counteract oxidative stress by antioxidants. CoQ is the only lipophilic antioxidant to be biosynthesized. Exogenous CoQ, however, protects cells from oxidative stress by conversion into its reduced antioxidant form by cellular reductases. The plasma membrane oxidoreductase and DT-diaphorase are two such systems, likewise, they are overexpressed under oxidative stress conditions.

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45

Isago, Hiroaki, and Yutaka Kagaya. "Synthesis and spectral properties of a dihydroxo(phthalocyaninato)antimony(V) complex." Journal of Porphyrins and Phthalocyanines 13, no. 03 (March 2009): 382–89. http://dx.doi.org/10.1142/s1088424609000474.

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The title complex cation, [ Sb ( pc )( OH )2]+, (pc = phthalocyaninate, C 32 H 16 N 82-) has been prepared by oxidizing [ Sb ( pc )] I 3 with tert-butyl perbenzoate and isolated as hexafluorophosphate and triflate salts. These salts are relatively well-soluble in polar solvents (e.g. CH 2 Cl 2, acetonitrile, acetone) without detectable aggregation. In particular, they dissolve relatively well in ethanol and methanol in which [ Sb ( pc ) Br 2]+ or [ Sb ( pc ) Cl 2]+ salts are poorly soluble whereas they have extremely low solubility in 1-chloronaphthalene and CHCl 3, unlike the bromo or chloro analogs. The spectral properties of [ Sb ( pc )( OH )2]+ have been investigated by optical absorption and magnetic circular dichroism spectroscopy. Although its Q band tends to appear at a longer wavelength in a solvent with a larger refractive index, as is the case for its Br and Cl analogs, the Q band positions in donor solvents deviate considerably from linear correlation between Onsager's solvent polarity function. In the Soret band region, spectra of [ Sb ( pc )( OH )2]+ are different in CH 2 Cl 2 and acetonitrile, particularly around the B1/B2 bands, unlike the bromo and chloro analogs. The solvent dependence of absorption spectra and the difference in solubility suggests that the presence of the axial hydroxyl groups endows the phthalocyanine macrocycle with considerable hydrophilicity. It also suggests that there are some specific chemical interactions between the axial hydroxyl groups and the surrounding donor solvent molecules.

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46

Nakajima, Hiraku. "$t$–analogs of $q$–characters of Kirillov-Reshetikhin modules of quantum affine algebras." Representation Theory of the American Mathematical Society 7, no. 12 (July 10, 2003): 259–74. http://dx.doi.org/10.1090/s1088-4165-03-00164-x.

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47

Sevost’yanov, E. A. "Removal of singularities and analogs of the Sokhotskii–Weierstrass theorem for Q-mappings." Ukrainian Mathematical Journal 61, no. 1 (January 2009): 140–53. http://dx.doi.org/10.1007/s11253-009-0190-4.

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48

Ismail, Mourad E. H., and Zeinab S. I. Mansour. "q-Analogs of Lidstone expansion theorem, two-point Taylor expansion theorem, and Bernoulli polynomials." Analysis and Applications 17, no. 06 (September 23, 2019): 853–95. http://dx.doi.org/10.1142/s0219530518500264.

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Abstract:

In this paper, we introduce a generalization of the [Formula: see text]-Taylor expansion theorems. We expand a function in a neighborhood of two points instead of one in three different theorems. The first is a [Formula: see text]-analog of the Lidstone theorem where the two points are 0 and 1 and we expand the function in [Formula: see text]-analogs of Lidstone polynomials which are in fact [Formula: see text]-Bernoulli polynomials as in the classical case. The definitions of these [Formula: see text]-Bernoulli polynomials and numbers are introduced. We also introduce [Formula: see text]-analogs of Euler polynomials and numbers. On the other two expansion theorems, we expand an analytic function around arbitrary points [Formula: see text] and [Formula: see text] either in terms of the polynomials [Formula: see text] or in terms of the polynomials [Formula: see text]. As an application, we introduce a new series expansion for the basic hypergeometric series [Formula: see text].

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49

Naik, Pradeep Kumar, Afroz Alam, Ashutosh Malhotra, and Owasis Rizvi. "Molecular Modeling and Structure-Activity Relationship of Podophyllotoxin and Its Congeners." Journal of Biomolecular Screening 15, no. 5 (May 10, 2010): 528–40. http://dx.doi.org/10.1177/1087057110368994.

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A quantitative structure-activity relationship (QSAR) model has been developed between cytotoxic activity and structural properties by considering a data set of 119 podophyllotoxin analogs based on 2D and 3D structural descriptors. A systematic stepwise searching approach of zero tests, a missing value test, a simple correlation test, a multicollinearity test, and a genetic algorithm method of variable selection was used to generate the model. A statistically significant model ( r train2 = 0.906; q cv2 = 0.893) was obtained with the molecular descriptors. The robustness of the QSAR model was characterized by the values of the internal leave-one-out cross-validated regression coefficient ( q cv2) for the training set and r test2 for the test set. The overall root mean square error (RMSE) between the experimental and predicted pIC50 value was 0.265 and r test2 = 0.824, revealing good predictability of the QSAR model. For an external data set of 16 podophyllotoxin analogs, the QSAR model was able to predict the tubulin polymerization inhibition and mechanistically cytotoxic activity with an RMSE value of 0.295 in comparison to experimental values. The QSAR model developed in this study shall aid further design of novel potent podophyllotoxin derivatives.

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50

Makarov, Sergey G., Olga N. Suvorova, and Dieter Wöhrle. "Conjugated di- and trinuclear phthalocyanines and their analogs." Journal of Porphyrins and Phthalocyanines 15, no. 09n10 (September 2011): 791–808. http://dx.doi.org/10.1142/s1088424611003835.

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Abstract:

Extended π-electron delocalization is the most important property of phthalocyanines and structurally related systems. The position of the longest wavelength absorption (Q-band) is influenced by the kind of substituents and by additional fused benzene rings at the ligand. Very large wavelength shifts are obtained with planar annulated di- and trinuclear phthalocyanine analogs sharing a common benzene ring which are the main point of this review. In addition, condensed di- and trinuclear phthalocyanines, and di- and trinuclear phthalocyanines linked via one or two carbon atoms of the macrocycles are discussed for comparison.

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