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Published: 10 March 2023

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1

CHATTERJEE, TAPAS. "THE STRONG CHOWLA–MILNOR SPACES AND A CONJECTURE OF GUN, MURTY AND RATH." International Journal of Number Theory 08, no. 05 (July 6, 2012): 1301–14. http://dx.doi.org/10.1142/s1793042112500765.

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In a recent work, Gun, Murty and Rath formulated the Strong Chowla–Milnor conjecture and defined the Strong Chowla–Milnor space. In this paper, we proved a non-trivial lower bound for the dimension of these spaces. We also obtained a conditional improvement of this lower bound and noted that an unconditional improvement of this lower bound will lead to irrationality of both ζ(k) and ζ(k)/πk for all odd positive integers k. Following Gun, Murty and Rath, we define generalized Zagier spaces Vp(K) for multiple zeta values over a number field K. We prove that the dimension of V4d+2(K) for d ≥ 1, is at least 2, assuming a conjecture of Gun, Murty and Rath.

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2

Cunningham, Bill, Penny Haxell, Bruce Richter, Nick Wormald, and Andrew Thomason. "To Adrian Bondy and U.S.R. Murty." Journal of Combinatorial Theory, Series B 90, no. 1 (January 2004): 1. http://dx.doi.org/10.1016/j.jctb.2003.10.001.

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3

Philip, Ligy, and S. Murty Bhallamudi. "Editorial Perspectives: innovation needs for the water sector in India to achieve sustainable development goals." Environmental Science: Water Research & Technology 5, no. 7 (2019): 1200–1201. http://dx.doi.org/10.1039/c9ew90026h.

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4

Ming, Huang Zhen. "Corrections to the differential inequalities by D. R. K. S. Rao, K. N. Murty, and M. S. N. Murty." Journal of Mathematical Analysis and Applications 116, no. 2 (June 1986): 528–30. http://dx.doi.org/10.1016/s0022-247x(86)80016-6.

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5

Cao, Chenghu, and Yongbo Zhao. "A Generalized Labeled Multi-Bernoulli Filter Based on Track-before-Detect Measurement Model for Multiple-Weak-Target State Estimate Using Belief Propagation." Remote Sensing 14, no. 17 (August 26, 2022): 4209. http://dx.doi.org/10.3390/rs14174209.

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In this paper, we propose the specific recursion formula for the generalized labeled multi-Bernoulli filter based on the track-before-detect strategy (GLMB-TBD) using a belief propagation algorithm. The proposed method aims to track multiple weak targets with superior performance. Compared to the Murty algorithm-based and Gibbs sampling-based implementation of GLMB-TBD filter, the proposed algorithm improves the tracking accuracy of multiple weak targets without pruning operation to preserve the relevant association information. The superior performance in tracking accuracy of the algorithm is validated for simulated scenarios using OSPA(2) metric. More importantly, the simulation results demonstrate that the proposed algorithm outputs both the Gibbs sampling-based version and Murty algorithm-based version in computational cost due to linear complex in the number of both Bernoulli components and measurements.

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6

Girstmair, Kurt. "On an Irreducibility Criterion of M. Ram Murty." American Mathematical Monthly 112, no. 3 (March 1, 2005): 269. http://dx.doi.org/10.2307/30037445.

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7

Girstmair, Kurt. "On an Irreducibility Criterion of M. Ram Murty." American Mathematical Monthly 112, no. 3 (March 2005): 269–70. http://dx.doi.org/10.1080/00029890.2005.11920194.

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8

Bennett, Anne. "Obituary: Dr Judith Anne Murty, MBChB, DRCOG, FFSRH." Journal of Family Planning and Reproductive Health Care 35, no. 4 (October 1, 2009): 263. http://dx.doi.org/10.1783/147118909789587213.

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9

Harte, Liam. ""Indian Philosophy: An Introduction," by M. Ram Murty." Teaching Philosophy 37, no. 2 (2014): 264–68. http://dx.doi.org/10.5840/teachphil201437216.

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10

Shukla, R. P., and Daniel Malacara. "Some applications of the Murty interferometer: A review." Optics and Lasers in Engineering 26, no. 1 (January 1997): 1–42. http://dx.doi.org/10.1016/0143-8166(95)00069-0.

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11

Van Steenbergen, Petra. "In memoriam for Prof. Tadepalli (Tad) Murty (1937–2018)." Natural Hazards 96, no. 2 (March 2019): 551–52. http://dx.doi.org/10.1007/s11069-019-03619-y.

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12

Blair, Charles. "Linear Complementarily, Linear and Nonlinear Programming (K. G. Murty)." SIAM Review 31, no. 2 (June 1989): 333–34. http://dx.doi.org/10.1137/1031068.

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13

Murty, A. S. Ramachandra, A. Mary Se]vam, B. K. Bandyopadhya, N. Revathi, A. G. Pillai, and Bh V. Ramana Murty. "Electrical and Microphysical Responses to Salt Seeding in Warm Maritime Cumulus Clouds." Journal of Weather Modification 13, no. 1 (October 14, 2012): 174–76. http://dx.doi.org/10.54782/jwm.v13i1.53.

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Electrical, microphysical and dynamical responses to salt seeding have been investigated during cloud seeding experiments in several parts of India. Following massive salt seeding, increases in cloud temperature by I to 2 Celsius and cloud liquid water content up to 200 percent were observed in warm cumulus clouds (Ramahandra Murty eta., 1975, 1976). Cloud drop size distributions in seeded warm cumulus clouds increased in mean volume diameter up to 478 percent and computed liquid water content increased upward of 60 percent (Kapoor et al., 1976). In maritime warm cumulus clouds, which developed rain following seeding, the electric field reversed from initial negative to positive, occasionally preceded by intensification (Ramachandra Murty et al., 1976). This field reversal was attributed to the transport of large positive charges, from upper cloud levels to the base, by raindrops which form initially at higher levels in vigorous updraft regions. The prior intensification was attributed to updraft invigoration produced by massive salt seeding, since electrical activity is closely associated with convective activity (Latham and Stow, 1969).

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14

Pacelli, Allison M. "A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible byn." Canadian Mathematical Bulletin 49, no. 3 (September 1, 2006): 448–63. http://dx.doi.org/10.4153/cmb-2006-044-7.

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AbstractIn this paper, we find a lower bound on the number of cyclic function fields of prime degreelwhose class numbers are divisible by a given integern. This generalizes a previous result of D. Cardon and R. Murty which gives a lower bound on the number of quadratic function fields with class numbers divisible byn.

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15

Green, Ronald. "On: “Nomogram for the direct interpretation of magnetic anomalies due to long horizontal cylinders,” by T. K. S. Prakasa Rao, M. Subrahmanyam, and A. Srikrishna Murty, (GEOPHYSICS, 51, 2156–2159, November 1986.)." GEOPHYSICS 52, no. 10 (October 1987): 1442–43. http://dx.doi.org/10.1190/1.1442259.

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In the article by T. K. S. Prakasa Rao, M. Subrahmanyam, and A. Srikrishna Murty, the trivial problem of interpreting the magnetic anomaly over a horizontal cylinder was examined and a set of nomograms to assist with the interpretation was presented. Prakasa Rao et al. begin their discussion with equation (1) from Gay (1965).

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16

Kuo, Wentang, Yu-Ru Liu, Sávio Ribas, and Kevin Zhou. "The Shifted Turán Sieve Method on Tournaments." Canadian Mathematical Bulletin 62, no. 4 (April 11, 2019): 841–55. http://dx.doi.org/10.4153/s000843951900016x.

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AbstractWe construct a shifted version of the Turán sieve method developed by R. Murty and the second author and apply it to counting problems on tournaments. More precisely, we obtain upper bounds for the number of tournaments which contain a fixed number of restricted $r$-cycles. These are the first concrete results which count the number of cycles over “all tournaments”.

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17

Bharadwaj, Abhishek T. "A short note on generalized Euler–Briggs constants." International Journal of Number Theory 16, no. 04 (December 18, 2019): 823–39. http://dx.doi.org/10.1142/s1793042120500426.

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Recently, Gun, Saha and Sinha had introduced the notion of generalised Euler–Briggs constant [Formula: see text] for a finite set of primes [Formula: see text]. In a subsequent work, Gun, Murty and Saha introduced the following [Formula: see text]-vector space [Formula: see text] and showed that [Formula: see text] In this note, we improve the lower bound, namely [Formula: see text]

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18

Hadjiloucas, S., G. C. Walker, and J. W. Bowen. "Extending Murty interferometry to the Terahertz part of the spectrum." Journal of Physics: Conference Series 307 (August 17, 2011): 012012. http://dx.doi.org/10.1088/1742-6596/307/1/012012.

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19

Dailly, Antoine, Florent Foucaud, and Adriana Hansberg. "Strengthening the Murty–Simon conjecture on diameter 2 critical graphs." Discrete Mathematics 342, no. 11 (November 2019): 3142–59. http://dx.doi.org/10.1016/j.disc.2019.06.023.

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20

Blair, Charles. "Linear Programming (Katta G. Murty) and Linear Programming (Vasek Chvaˇtal)." SIAM Review 27, no. 1 (March 1985): 91–93. http://dx.doi.org/10.1137/1027020.

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21

Aksenov, Sergey A., Eugene N. Chumachenko, and Irina V. Logashina. "Tensile Testing of Ti-6Al-4V Alloy Superplasticity." Materials Science Forum 762 (July 2013): 392–97. http://dx.doi.org/10.4028/www.scientific.net/msf.762.392.

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This paper presents the research on the flow characteristics of the Ti-6V-4Al alloy in wide ranges of temperature (725 ‑ 950 °C) and strain rate (10-5 ‑ 10-2 s-1). The material processing maps were constructed based on the basis of dynamic materials model (DMM) developed by Prassad and modified by Narayana Murty. For the construction of such maps the data of the material flow stress at different temperatures and strain rates is necessary. To obtain such data the stepped tensile tests which allow obtaining the stress - strain rate dependence at a given temperature are ideal. The experiments conducted consist of the tensile test series at various temperatures with stepped change of the deformation rate. By the results of these tests the constitutive equations, which describe relationship between stress and strain rate for each temperature, were obtained. The data was analyzed in terms of the two different approaches proposed by Prassad and Narayana Murty to assess the impact of deformation conditions on the formability and flow stability of the material. Based on these approaches, the processing maps, which enable identifying the conditions of the Ti-6V-4Al alloy superplasticity, were constructed.

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22

GHITZA, ALEXANDRU. "DISTINGUISHING HECKE EIGENFORMS." International Journal of Number Theory 07, no. 05 (August 2011): 1247–53. http://dx.doi.org/10.1142/s1793042111004708.

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We revisit a theorem of Ram Murty about the number of initial Fourier coefficients that two cuspidal eigenforms of different weights can have in common. We prove an explicit upper bound on this number, and give better conditional and unconditional asymptotic upper bounds. Finally, we describe a numerical experiment testing the sharpness of the upper bound in the case of forms of level one.

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23

Ram Murty, M. "Elliptic Curves and Modular Forms." Canadian Mathematical Bulletin 34, no. 3 (September 1, 1991): 375–84. http://dx.doi.org/10.4153/cmb-1991-060-4.

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AbstractThis is a survey of some recent developments in the theory of elliptic curves. After an informal discussion of the main theorems of the arithmetic side of the theory and the open problems confronting the subject, we describe the recent work of K. Rubin, V. Koly vagin, K. Murty and the author which establishes the finiteness of the Shafarevic-Tate group for modular elliptic curves of rank zero and one.

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24

Saha, Biswajyoti. "A note on arithmetical functions with absolutely convergent Ramanujan expansions." International Journal of Number Theory 12, no. 06 (July 26, 2016): 1595–611. http://dx.doi.org/10.1142/s1793042116500974.

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Arithmetical functions with absolutely convergent Ramanujan expansions have been recently studied in certain contexts, by the present author, Murty and many others. In this article, we aim to weaken some of their hypotheses and derive asymptotic formulas with an explicit error term for sums of the form [Formula: see text] and [Formula: see text] where [Formula: see text] and [Formula: see text] are two arithmetical functions with absolutely convergent Ramanujan expansion.

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25

Clark, David A., and Masato Kuwata. "Generalized Artin'S Conjecture for Primitive Roots and Cyclicity Mod of Elliptic Curves Over Function Fields." Canadian Mathematical Bulletin 38, no. 2 (June 1, 1995): 167–73. http://dx.doi.org/10.4153/cmb-1995-023-2.

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AbstractLet k = Fq be a finite field of characteristic p with q elements and let K be a function field of one variable over k. Consider an elliptic curve E defined over K. We determine how often the reduction of this elliptic curve to a prime ideal is cyclic. This is done by generalizing a result of Bilharz to a more general form of Artin's primitive roots problem formulated by R. Murty.

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26

TANABE, NAOMI. "NON-VANISHING OF DERIVATIVES OF L-FUNCTIONS ATTACHED TO HILBERT MODULAR FORMS." International Journal of Number Theory 08, no. 04 (May 16, 2012): 1099–105. http://dx.doi.org/10.1142/s1793042112500662.

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This paper is to show a non-vanishing property of the derivative of certain L-functions. For certain primitive holomorphic Hilbert modular forms, if the central critical value of the standard L-function does not vanish, then neither does its derivative. This is a generalization of a result by Gun, Murty and Rath in the case of elliptic modular forms. Some applications in transcendental number theory deduced from this result are discussed as well.

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27

Godbole, Vanshree. "Sudha Murty`s ‘Three Thousand Stitches’: A Chronicle of Social Reformations." International Journal of English Literature and Social Sciences 5, no. 4 (2020): 849–52. http://dx.doi.org/10.22161/ijels.54.3.

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28

Cojocaru, Alina Carmen, and Chantal David. "Frobenius fields for Drinfeld modules of rank 2." Compositio Mathematica 144, no. 4 (July 2008): 827–48. http://dx.doi.org/10.1112/s0010437x07003387.

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AbstractLet ϕ be a Drinfeld module of rank 2 over the field of rational functions $F=\mathbb {F}_q(T)$, with $\mathrm {End}_{\bar {F}}(\phi ) = \mathbb {F}_q[T]$. Let K be a fixed imaginary quadratic field over F and d a positive integer. For each prime $\mathfrak {p}$ of good reduction for ϕ, let $\pi _{\mathfrak {p}}(\phi )$ be a root of the characteristic polynomial of the Frobenius endomorphism of ϕ over the finite field $\mathbb {F}_q[T] / \mathfrak {p}$. Let Πϕ(K;d) be the number of primes $\mathfrak {p}$ of degree d such that the field extension $F(\pi _{\mathfrak {p}}(\phi ))$ is the fixed imaginary quadratic field K. We present upper bounds for Πϕ(K;d) obtained by two different approaches, inspired by similar ones for elliptic curves. The first approach, inspired by the work of Serre, is to consider the image of Frobenius in a mixed Galois representation associated to K and to the Drinfeld module ϕ. The second approach, inspired by the work of Cojocaru, Fouvry and Murty, is based on an application of the square sieve. The bounds obtained with the first method are better, but depend on the fixed quadratic imaginary field K. In our application of the second approach, we improve the results of Cojocaru, Murty and Fouvry by considering projective Galois representations.

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29

Haynes, Teresa W., Michael A. Henning, Lucas C. van der Merwe, and Anders Yeo. "On a conjecture of Murty and Simon on diameter 2-critical graphs." Discrete Mathematics 311, no. 17 (September 2011): 1918–24. http://dx.doi.org/10.1016/j.disc.2011.05.007.

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30

Matsuda, K., M. Namiki, and T. H. Barnes. "A differential interference contrast system incorporating a Murty interferometer and holographic correction." Optics and Lasers in Engineering 9, no. 1 (January 1988): 35–46. http://dx.doi.org/10.1016/0143-8166(88)90027-9.

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31

Zaman, Asif. "The least unramified prime which does not split completely." Forum Mathematicum 30, no. 3 (May 1, 2018): 651–61. http://dx.doi.org/10.1515/forum-2017-0081.

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AbstractLet {K/F} be a finite extension of number fields of degree {n\geq 2}. We establish effective field-uniform unconditional upper bounds for the least norm of a prime ideal {\mathfrak{p}} of F which is degree 1 over {\mathbb{Q}} and does not ramify or split completely in K. We improve upon the previous best known general estimates due to Li [7] when {F=\mathbb{Q}}, and Murty and Patankar [9] when {K/F} is Galois. Our bounds are the first when {K/F} is not assumed to be Galois and {F\neq\mathbb{Q}}.

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32

Danchick, R., and G. E. Newnam. "Reformulating Reid's MHT method with generalised Murty K-best ranked linear assignment algorithm." IEE Proceedings - Radar, Sonar and Navigation 153, no. 1 (2006): 13. http://dx.doi.org/10.1049/ip-rsn:20050041.

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33

Sebastian, C. D. "The Heterodox Insider K. Satchidananda Murty: A Critique of His The Indian Spirit." Journal of Indian Council of Philosophical Research 34, no. 1 (November 3, 2016): 33–49. http://dx.doi.org/10.1007/s40961-016-0074-6.

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34

Haynes, Teresa W., Michael A. Henning, and Anders Yeo. "On a conjecture of Murty and Simon on diameter two critical graphs II." Discrete Mathematics 312, no. 2 (January 2012): 315–23. http://dx.doi.org/10.1016/j.disc.2011.09.022.

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35

Haynes, Teresa W., Michael A. Henning, Lucas C. van der Merwe, and Anders Yeo. "Progress on the Murty–Simon Conjecture on diameter-2 critical graphs: a survey." Journal of Combinatorial Optimization 30, no. 3 (August 31, 2013): 579–95. http://dx.doi.org/10.1007/s10878-013-9651-7.

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36

Cojocaru, Alina Carmen, and Andrew Michael Shulman. "The Distribution of the First Elementary Divisor of the Reductions of a Generic Drinfeld Module of Arbitrary Rank." Canadian Journal of Mathematics 67, no. 6 (December 1, 2015): 1326–57. http://dx.doi.org/10.4153/cjm-2015-006-9.

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AbstractLet ψ be a generic Drinfeld module of rank r ≥ 2. We study the first elementary divisor d1,℘ (ψ) of the reduction of ψ modulo a prime ℘, as ℘ varies. In particular, we prove the existence of the density of the primes ℘ for which d1,℘ (ψ) is fixed. For r = 2, we also study the second elementary divisor (the exponent) of the reduction of ψ modulo ℘ and prove that, on average, it has a large norm. Our work is motivated by J.-P. Serre's study of an elliptic curve analogue of Artin's Primitive Root Conjecture, and, moreover, by refinements to Serre's study developed by the first author and M. R. Murty.

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37

Fu, Honghao. "Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimension." Quantum 6 (January 3, 2022): 614. http://dx.doi.org/10.22331/q-2022-01-03-614.

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Let p be an odd prime and let r be the smallest generator of the multiplicative group Zp∗. We show that there exists a correlation of size Θ(r2) that self-tests a maximally entangled state of local dimension p−1. The construction of the correlation uses the embedding procedure proposed by Slofstra (Forum of Mathematics, Pi. (2019)). Since there are infinitely many prime numbers whose smallest multiplicative generator is in the set {2,3,5} (D.R. Heath-Brown The Quarterly Journal of Mathematics (1986) and M. Murty The Mathematical Intelligencer (1988)), our result implies that constant-sized correlations are sufficient for self-testing of maximally entangled states with unbounded local dimension.

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38

Canales Pacheco, Benito. "Sensor nulo de Shack-Hartmann para evaluar una superficie cóncava esférica y una parabólica / Null Shack-Hartmann Sensor for evaluating a concave spherical surface and a satellite dish." RECI Revista Iberoamericana de las Ciencias Computacionales e Informática 4, no. 8 (January 14, 2016): 49. http://dx.doi.org/10.23913/reci.v4i8.32.

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Actualmente existen muchas pruebas ópticas que analizan una superﬁcie o un sistema óptico. Según la literatura científica las hay de dos clases, dependiendo del método que utilicen: las denominadas no interferométrícas, es decir, la prueba de Hartmann, Alambre, Estrella, Foucault, Ronchi [1]. Dichas pruebas permiten obtener información sobre la derivada del frente de onda (∂w/∂y). Por otro lado, están las denominadas pruebas interferométricas, por ejemplo: el Interferómetro de Tyman Green, Fizeau, Newton, Murty (desplazamiento lateral) [2]. Con este tipo de pruebas se obtiene información directa del frente de onda (W). El presente trabajo utiliza el principio físico de la prueba de Hartmann para construir un sensor de frente de onda tipo Shack-Hartmann, que permita evaluar una superficie óptica esférica y una parabólica.

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39

Bhat, Mahadev G. "Environmental Valuation in South Asia, edited by A.K. Enamul Haque, M.N. Murty, and Priya Shyamsundar." Journal of Natural Resources Policy Research 5, no. 1 (January 2013): 67–68. http://dx.doi.org/10.1080/19390459.2013.763323.

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40

Srivastava, S. N., M. S. Tomar, and R. S. Kasana. "Determination of the linear thermal expansion coefficient of long metallic bars by Murty shearing interferometer." Optics & Laser Technology 22, no. 4 (August 1990): 283–86. http://dx.doi.org/10.1016/0030-3992(90)90062-9.

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41

An, Zhen, Jin-Shan Li, and Yong Feng. "Optimization of thermal processing parameters of Ti555211 alloy using processing maps based on Murty criterion." Rare Metals 35, no. 2 (November 28, 2015): 154–61. http://dx.doi.org/10.1007/s12598-015-0655-6.

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42

Horen, Jeff. "Linear programming, by Katta G. Murty, John Wiley & Sons, New York, 1983, 482 pp." Networks 15, no. 2 (1985): 273–74. http://dx.doi.org/10.1002/net.3230150211.

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43

Harwood, B., and C. L. Rice. "Changes in motor unit recruitment thresholds of the human anconeus muscle during torque development preceding shortening elbow extensions." Journal of Neurophysiology 107, no. 10 (May 15, 2012): 2876–84. http://dx.doi.org/10.1152/jn.00902.2011.

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Rate of torque development and the subsequent movement velocity are modulated by motor unit (MU) properties, primarily MU discharge rate and MU recruitment threshold (MURT). In isometric conditions, MURTs have been shown to decrease with increased rates of torque development. It is unclear whether this relationship is similar in the production of dynamic shortening contractions. Using fast joint velocities to drive the system, we aimed to determine how anconeus MURTs recorded during the torque production phase preceding movement were affected in relation to the resultant peak elbow extension velocity. Recruitment thresholds of 17 MUs from 9 young men were tracked throughout non-isokinetic dynamic elbow extensions with velocities ranging from 64°/s to 500°/s at a constant resistance of 25% of maximal voluntary isometric contraction and during isometric elbow extensions (0°/s). Relative MURTs decreased ∼50% from the slowest (<25% of maximal velocity) to the fastest (>75% of maximal velocity) resultant velocity ranges ( P < 0.05). Although a significant ( P < 0.001) but weak ( r = −0.27, R2 = 0.08) relationship was observed between MURT and resultant peak elbow extension velocity for the group, only 7 of the 17 MUs displayed significant moderate ( r = −0.40, R2 = 0.17) to strong ( r = −0.85, R2 = 0.73) negative MURT-velocity relationships. These data indicate variable responses of MURTs with increasing resultant peak velocity, which may be related to the intrinsic properties of individual MUs.

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44

Ouyang, Yi, and Jianfeng Xie. "The growth of Tate–Shafarevich groups in cyclic extensions." Compositio Mathematica 158, no. 10 (October 2022): 2014–32. http://dx.doi.org/10.1112/s0010437x22007734.

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Let $p$ be a prime number. Kęstutis Česnavičius proved that for an abelian variety $A$ over a global field $K$ , the $p$ -Selmer group $\mathrm {Sel}_{p}(A/L)$ grows unboundedly when $L$ ranges over the $(\mathbb {Z}/p\mathbb {Z})$ -extensions of $K$ . Moreover, he raised a further problem: is $\dim _{\mathbb {F}_{p}} \text{III} (A/L) [p]$ also unbounded under the above conditions? In this paper, we give a positive answer to this problem in the case $p \neq \mathrm {char}\,K$ . As an application, this result enables us to generalize the work of Clark, Sharif and Creutz on the growth of potential $\text{III}$ in cyclic extensions. We also answer a problem proposed by Lim and Murty concerning the growth of the fine Tate–Shafarevich groups.

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45

ROBERTS, D. F. "Indian Journal of Human Genetics. Edited by J. S. Murty. (Indian Society of Human Genetics, Hyderabad.)." Journal of Biosocial Science 29, no. 1 (January 1997): 119–28. http://dx.doi.org/10.1017/s0021932097231196.

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46

Wang, Sophia. "Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 9, No. 3." Journal of Mathematics Research 9, no. 3 (May 30, 2017): 112. http://dx.doi.org/10.5539/jmr.v9n3p112.

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Journal of Mathematics Research wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.Many authors, regardless of whether Journal of Mathematics Research publishes their work, appreciate the helpful feedback provided by the reviewers.Reviewers for Volume 9, Number 3 Ali Berkol, TurkeyArman Aghili, IranCecilia Maria Fernandes Fonseca, PortugalCecilia Rosa, PortugalChung-Chuan Chen, TaiwanGane Sam Lo, SenegalKong Liang, USAMarek Brabec, Czech RepublicMaria Alessandra Ragusa, ItalyMohammad Mehdi Rashidi, ChinaMohd Hafiz, MalaysiaN. V. Ramana Murty, IndiaÖzgür Ege, TurkeyPhilip Philipoff, BulgariaRovshan Bandaliyev, AzerbaijanSanjib Kumar Datta, IndiaSelcuk Koyuncu, USASergiy Koshkin, USAShenghua Ni, USAVishnu Narayan Mishra, IndiaXinyun Zhu, USAYibin Zhang, ChinaYifan Wang, USAYoussef El-Khatib, United Arab EmiratesZhongming Wang, USA Sophia WangOn behalf of,The Editorial Board of Journal of Mathematics ResearchCanadian Center of Science and Education

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47

Wu, Xia, and Yan Qin. "Rational Points of Elliptic Curve y2=x3+k3." Algebra Colloquium 25, no. 01 (January 22, 2018): 133–38. http://dx.doi.org/10.1142/s1005386718000081.

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Let E be an elliptic curve defined over the field of rational numbers ℚ. Let d be a square-free integer and let Ed be the quadratic twist of E determined by d. Mai, Murty and Ono have proved that there are infinitely many square-free integers d such that the rank of Ed(ℚ) is zero. Let E(k) denote the elliptic curve y2 = x3 + k. Then the quadratic twist E(1)d of E(1) by d is the elliptic curve [Formula: see text]. Let r = 1, 2, 5, 10, 13, 14, 17, 22. Ono proved that there are infinitely many square-free integers d ≡ r (mod 24) such that rank [Formula: see text], using the theory of modular forms. In this paper, we use the class number of quadratic field and Pell equation to describe these square-free integers k such that E(k3)(ℚ) has rank zero.

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48

GUO, Sheng-li, De-fu LI, Dong CHEN, and Hao-wei WANG. "Characterization of deformation stability of in-situ TiB2/6351 composites during hot compression based on Murty criterion." Transactions of Nonferrous Metals Society of China 20, no. 2 (February 2010): 267–75. http://dx.doi.org/10.1016/s1003-6326(09)60133-3.

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49

Killworth, P. D. "Numerical Modeling of Ocean Dynamics. By Z. KOWALIK and T. S. MURTY. World Scientific, 1993. 481 pp. £49." Journal of Fluid Mechanics 282 (January 10, 1995): 407. http://dx.doi.org/10.1017/s0022112095240187.

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Wang, Sophia. "Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 10, No. 1." Journal of Mathematics Research 10, no. 1 (January 29, 2018): 143. http://dx.doi.org/10.5539/jmr.v10n1p143.

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Journal of Mathematics Research wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.Many authors, regardless of whether Journal of Mathematics Research publishes their work, appreciate the helpful feedback provided by the reviewers.Reviewers for Volume 10, Number 1 Alan Jalal Abdulqader, Al-Mustansiriyah University, IraqArman Aghili, University of Guilan, IranGane Sam Lo, Universite Gaston Berger de Saint-Louis, SenegalIvan Drazic, University of Rijeka, CroatiaKong Liang, University of Illinois at Springfield, USAMeltem Erden Ege, Manisa Celal Bayar University, TurkeyMohammad A. AlQudah, German Jordanian University, JordanMohammad Sajid, Qassim University, Saudi ArabiaN. V. Ramana Murty, Andhra Loyola College, IndiaOmur Deveci, Kafkas University, TurkeyÖzgür Ege, Celal Bayar University, TurkeyPaul J. Udoh, University of Uyo, NigeriaRami Ahmad El-Nabulsi, Athens Institute for Education and Research, GreeceSanjib Kumar Datta, University of Kalyani, IndiaSergiy Koshkin, University of Houston Downtown, USAVinodh Kumar Chellamuthu, Dixie State University, USAZhongming Wang, Florida International University, USA Sophia WangOn behalf of,The Editorial Board of Journal of Mathematics ResearchCanadian Center of Science and Education

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