General Formulas for Evaluation of Singular Modulus of the Complete Elliptic Integral

K. R. Vasuki,G. Sharath,N. Bhaskar 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.1

The complete elliptic integral of the first kind K(k) is defined for 0 < k < 1 by K(k) := π /2Ɵ=0dƟ/√1 − k2 sin2 ƟThe real number k is called the modulus of the elliptic integral. The complementary modulus is k' = √1 − k2 (0 < k' < 1). Let ⋋ be a positive integer. The equation K(k') = √K(k),defines a unique real number k(k') (0 < k' < 1) called the singular modulus of K(k). In this paper, we establish certain general formulas for evaluating k(λ), by employing Ramanujan’s modular equation.

망상내피계의 기능이 Cryptococcus Neoformans의 감염에 미치는 효과에 관한 실험적 연구

서강석,이중달,안도철,박영림,김익형 부산의대 1968 부산의대잡지 - 부산대학교 의과대학 Vol.8 No.1

PCR - RFLP 기법을 이용해 젖소개량을 위한 유전적 표지로서 K- Casein 좌위의 유전자형 분석

정의룡(E . R . Chung),김우태(W . T . Kim),최석호(S . H . Choi),임태진(T . J . Rhim),한상기(S . K . Han) 한국축산학회 1995 한국축산학회지 Vol.37 No.1

Genotypes of K-casein(K-CN) locus as a genetic marker linked to quantitative trait loci affecting traits of economic importance in dairy cattle were determined by PCR-RFLP method. Genomic DNA was prepared from blood of Holstein cows. The PCR was used to amplify an 874 by region between nucleotides 10592 and 11466 from exon IV to intron IV of the bovine K-CN gene using sense primer(5`-GTGCTGAGTAGGTATCCTAG-3`) and antisense primer(5`GTAGAGTGCAACAACACTGG-3`). After amplification, PCR products were digested with four restriction enzymes, Hind III, Rsa I, Taq I, and Pst I, and the fragments were separated by agarose gel electrophoresis for RFLP analysis of K-CN locus. In addition to screening for the known Hind III and Rsa I restriction site polymorphisms of K-CN locus, we have found additional RFLPs specific for the K-CN A and B alleles in Taca I and Pst I enzymes. The amplified DNA product digested with each restriction enzyme generated specific RFLP pattern that allowed precise identification of K-CN AA, BB or AB genotypes. The K-CN genotypes determined for cows by the PCR-RFLP method agreed completely with the phenotypes obtained from milk samples of the same individuals. Thus, PCR amplification and RFLP analysis was shown to be a rapid and sensitive method for the discrimination of K-CN genotypes directly at the DNA level in dairy cattle of any age or sex. Consequently, the PCR-RFLP method presented in this study can be used as a valuable tool for early selection of AI bulls and calves with desirable K-CN B gene or K-CN BB genotype affecting superior milk production traits for genetic improvement of Holstein dairy cattle.

A note on vertex pair sum $k$-zero ring labeling

Antony Sanoj Jerome,K.R. Santhosh Kumar,T.J. Rajesh Kumar 한국전산응용수학회 2024 Journal of applied mathematics & informatics Vol.42 No.2

Let $G=(V,E)$ be a graph with $p$-vertices and $q$-edges and let $R^{\circ}$ be a finite zero ring of order $n$. An injective function $f:V(G)\to \{r_1,r_2,\ldots,r_k\}$, where $r_i\in R^\circ$ is called vertex pair sum $k$-zero ring labeling, if it is possible to label the vertices $x\in V$ with distinct labels from $R^{\circ}$ such that each edge $e=uv$ is labeled with $f(e=uv)=[f(u)+f(v)] \pmod n$ and the edge labels are distinct. A graph admits such labeling is called vertex pair sum $k$-zero ring graph. The minimum value of positive integer $k$ for a graph $G$ which admits a vertex pair sum $k$-zero ring labeling is called the vertex pair sum $k$-zero ring index denoted by $\psi_{pz}(G)$. In this paper, we defined the vertex pair sum $k$-zero ring labeling and applied to some graphs.

Effect of potassium addition on bimetallic PtSn supported θ-Al₂O₃ catalyst for n-butane dehydrogenation to olefins

Nagaraja, B.M.,Jung, H.,Yang, D.R.,Jung, K.D. Elsevier Science Publishers 2014 CATALYSIS TODAY - Vol.232 No.-

PtSn/θ-Al<SUB>2</SUB>O<SUB>3</SUB> catalysts with different amount of potassium (0.4, 0.7, 0.95, 1.2 and 1.45wt.%) were prepared by an impregnation method, and their catalytic activity in n-butane dehydrogenation was investigated at 823K, an atmospheric pressure and a GHSV of 18,000mL(g<SUB>cat</SUB>h)<SUP>-1</SUP>. The compositions listed in order of n-C<SUB>4</SUB><SUP>=</SUP> yields at 823K were as follows: K<SUB>0.95</SUB>(PtSn)<SUB>1.5</SUB>>(PtSn)<SUB>1.5</SUB>>K<SUB>0.4</SUB>(PtSn)<SUB>1.5</SUB>>K<SUB>0.7</SUB>(PtSn)<SUB>1.5</SUB>>K<SUB>1.2</SUB>(PtSn)<SUB>1.5</SUB>>K<SUB>1.45</SUB>(PtSn)<SUB>1.5</SUB>>K<SUB>0.9</SUB>(Pt)<SUB>1.5</SUB>. The K<SUB>0.9</SUB>(Pt)<SUB>1.5</SUB> and K<SUB>0.95</SUB>(Sn)<SUB>1.5</SUB> catalyst severely deactivated in n-butane dehydrogenation. The (PtSn)<SUB>1.5</SUB> (without K) catalyst showed the highest n-butane conversion, while K<SUB>0.95</SUB>(PtSn)<SUB>1.5</SUB> did the highest n-C<SUB>4</SUB><SUP>=</SUP> yield. The small amount of potassium on bimetallic PtSn/θ-Al<SUB>2</SUB>O<SUB>3</SUB> catalyst improved n-C<SUB>4</SUB><SUP>=</SUP> selectivity, but slightly decreased n-butane conversion, resulting in the increase of n-C<SUB>4</SUB><SUP>=</SUP> yield. The effect of potassium was caused by blocking the acid sites of Pt catalyst. The TPR and HAADF STEM-EDS study suggested the reduction procedure of the Pt, Sn and K species. However, the higher loaded potassium (1.2 and 1.45wt.%) doped (PtSn)<SUB>1.5</SUB> catalysts were rather highly deactivated because the sizes of Pt particles were increased by weakening the interaction between Pt and Sn. The n-C<SUB>4</SUB><SUP>=</SUP> selectivity of the (PtSn)<SUB>1.5</SUB> catalyst increased with respect to the reaction, while that of the potassium doped catalysts maintained the high n-C<SUB>4</SUB><SUP>=</SUP> selectivity from the beginning of the reaction. Also, different alkali metals (Ca, Na and Li) were tested for the comparison with K. The potassium doped catalyst showed the highest n-C<SUB>4</SUB><SUP>=</SUP> yield among the other alkali metals for n-butane dehydrogenation.

Robust MR assessment of cerebral blood volume and mean vessel size using SPION-enhanced ultrashort echo acquisition

Han, S.H.,Cho, J.H.,Jung, H.S.,Suh, J.Y.,Kim, J.K.,Kim, Y.R.,Cho, G.,Cho, H. Elsevier 2015 NeuroImage Vol.112 No.-

<P><B>Abstract</B></P> <P>Intravascular superparamagnetic iron oxide nanoparticles (SPION)-enhanced MR transverse relaxation rates (∆<I>R<SUB>2</SUB> <SUP>⁎</SUP> </I> and ∆<I>R<SUB>2</SUB> </I>) are widely used to investigate <I>in vivo</I> vascular parameters, such as the cerebral blood volume (CBV), microvascular volume (MVV), and mean vessel size index (mVSI, ∆<I>R<SUB>2</SUB> <SUP>⁎</SUP>/∆R<SUB>2</SUB> </I>). Although highly efficient, regional comparison of vascular parameters acquired using gradient-echo based <I>∆R<SUB>2</SUB> <SUP>⁎</SUP> </I> is hampered by its high sensitivity to magnetic field perturbations arising from air–tissue interfaces and large vessels. To minimize such demerits, we took advantage of the dual contrast property of SPION and both theoretically and experimentally verified the direct benefit of replacing gradient-echo based <I>∆R<SUB>2</SUB> <SUP>⁎</SUP> </I> measurement with ultra-short echo time (UTE)-based <I>∆R<SUB>1</SUB> </I> contrast to generate the robust CBV and mVSI maps. The UTE acquisition minimized the local measurement errors from susceptibility perturbations and enabled dose-independent CBV measurement using the vessel/tissue <I>∆R<SUB>1</SUB> </I> ratio, while independent spin-echo acquisition enabled simultaneous <I>∆R<SUB>2</SUB> </I> measurement and mVSI calculation of the cortex, cerebellum, and olfactory bulb, which are animal brain regions typified by significant susceptibility-associated measurement errors.</P> <P><B>Highlights</B></P> <P> <UL> <LI> <I>ΔR<SUB>2</SUB> <SUP>⁎</SUP> </I>-CBV is vessel orientation dependent and vulnerable to susceptibility artifacts. </LI> <LI> UTE acquisition minimizes susceptibility artifacts and enables dose-independent CBV. </LI> <LI> UTE-based CBV can theoretically and experimentally replace <I>ΔR<SUB>2</SUB> <SUP>⁎</SUP> </I> for vessel size. </LI> <LI> UTE-based <I>ΔR<SUB>1</SUB> </I> contrasts enable consistent CBV and mVSI maps in mouse brain. </LI> <LI> <I>ΔR<SUB>1</SUB> </I> and <I>ΔR<SUB>2</SUB> <SUP>⁎</SUP> </I> contrasts can be synergistically combined to enhance SPION contrast. </LI> </UL> </P>

CLASS OF MAPPINGS BETWEEN R_z-SUPERCONTINUOUS FUNCTIONS AND R_δ-SUPERCONTINUOUS FUNCTIONS

( A. R. Prasannan ),( Jeetendra Aggarwal ),( A. K. Das ),( Jayanta Biswas ) 호남수학회 2017 호남수학학술지 Vol.39 No.4

A new class of functions called R_θ-supercontinuous functions is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity, which already exist in the literature, is elaborated. The class of R_θ-supercontinuous functions properly contains the class of R_z-supercontinuous functions [39] which in turn properly contains the class of R_cl-supercontinuous functions [43] and so includes all cl-supercontinuous (clopen continuous) functions ([38], [34]) and is properly contained in the class of R_δ-supercontinuous functions [24].

Photoproduction of the_f1(1285)meson

Dickson, R.,Schumacher, R. A.,Adhikari, K. P.,Akbar, Z.,Amaryan, M. J.,Anefalos Pereira, S.,Badui, R. A.,Ball, J.,Battaglieri, M.,Batourine, V.,Bedlinskiy, I.,Biselli, A.,Boiarinov, S.,Briscoe, W. J. American Physical Society 2016 Physical Review C Vol.93 No.6

<P>The f(1)(1285) meson withmass 1281.0 +/- 0.8MeV/c(2) and width 18.4 +/- 1.4MeV (full width at half maximum) was measured for the first time in photoproduction from a proton target using CLAS at Jefferson Lab. Differential cross sections were obtained via the eta pi(+)pi(-), K+(K) over bar (0) pi(-), and (K-K0)pi(+) decay channels from threshold up to a center-of-mass energy of 2.8 GeV. The mass, width, and an amplitude analysis of the eta pi(+)pi(-) final-state Dalitz distribution are consistent with the axial-vector J(P) = 1(+) f(1)(1285) identity, rather than the pseudoscalar 0(-) eta(1295). The production mechanism is more consistent with s-channel decay of a high-mass N* state and not with t-channel meson exchange. Decays to eta pi pi go dominantly via the intermediate a(0)(+/-) (980)pi(-/+) states, with the branching ratio Gamma [a(0)pi (no (K) over barK)]/Gamma[eta pi pi (all)] = 0.74 +/- 0.09. The branching ratios Gamma (K (K) over bar pi)/Gamma(eta pi pi) = 0.216 +/- 0.033 and Gamma (gamma rho(0))/Gamma(eta pi pi) = 0.047 +/- 0.018 were also obtained. The first is in agreement with previous data for the f(1)(1285), while the latter is lower than the world average.</P>

The partitioned-layer index: Answering monotone top-k queries using the convex skyline and partitioning-merging technique

Heo, J.S.,Whang, K.Y.,Kim, M.S.,Kim, Y.R.,Song, I.Y. North-Holland [etc ; Elsevier Science Ltd 2009 Information sciences Vol.179 No.19

A top-k query returns k tuples with the highest (or the lowest) scores from a relation. The score is computed by combining the values of one or more attributes. We focus on top-k queries having monotone linear score functions. Layer-based methods are well-known techniques for top-k query processing. These methods construct a database as a single list of layers. Here, the ith layer has the tuples that can be the top-i tuple. Thus, these methods answer top-k queries by reading at most k layers. Query performance, however, is poor when the number of tuples in each layer (simply, the layer size) is large. In this paper, we propose a new layer-ordering method, called the Partitioned-Layer Index (simply, the PL Index), that significantly improves query performance by reducing the layer size. The PL Index uses the notion of partitioning, which constructs a database as multiple sublayer lists instead of a single layer list subsequently reducing the layer size. The PL Index also uses the convex skyline, which is a subset of the skyline, to construct a sublayer to further reduce the layer size. The PL Index has the following desired properties. The query performance of the PL Index is quite insensitive to the weights of attributes (called the preference vector) of the score function and is approximately linear in the value of k. The PL Index is capable of tuning query performance for the most frequently used value of k by controlling the number of sublayer lists. Experimental results using synthetic and real data sets show that the query performance of the PL Index significantly outperforms existing methods except for small values of k (say, k=<9).

Best k-digit Rational Approximations ― True Versus Convergent-, Decimal-based Ones: Quality, Cost, Scope

S. K. Sen,R. P. Agarwal,G. A. Shaykhian 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.19 No.1

A k-digit rational approximation of an irrational number is defined as the rational number with k digits in the numerator. The actual best k digit rational approximation is unique and is the true/absolute one. The best k - digit rational approximation, when it exists, obtained from the convergents of the continued fraction representation of an irrational number is also unique and need not be the same as the absolute one. The best k digit decimal number for the irrational number is also unique but is not the true best k - digit rational approximation, in general. We discuss here the quality implying error, the cost implying computational/time complexity, and scope implying a possible usage/application of the concerned three computational algorithms.