An Analysis of Exports and Growth in Pakistan

The paper examines the export-led growth (ELG) paradigm for Pakistan, using data of the period from 1970-71 to 2003-04. The paper uses a number of analytical tools, including Unit Root Test, Phillips- Perron Tests, Co-integration Johansen Test, and the Granger Tests. The paper sets three hypotheses for testing the ELG paradigm for Pakistan; (a) whether GDP and exports are cointegrated, (b) whether exports Granger cause growth, and (c) whether exports Granger cause investment. The time series data on GDP growth, export growth and investment GDP ratio (proxy for capital formation), and the labour employed were used. The data were tested for stationarity using the Augmented Dickey-Fuller (ADF) test and Phillips-Perron test (1988), and then the relationship between GDP growth rate and the growth rate of other variables was determined using OLS with AR (1). The major finding of the present study is that growth rate of export, total investment, and labour employed have positively affected the GDP growth rate

Theoretical studies on structural and decay properties of Z=119Z=119 superheavy nuclei

In this manuscript, we analyze the structural properties of $Z=119$ superheavy nuclei in the mass range of 284 $\le$ A $\le$ 375 within the framework of deformed relativistic mean field theory (RMF) and calculate the binding energy, radii, quadrupole deformation parameter, separation energies and density profile. Further, a competition between possible decay modes such as $\alpha-$decay, $\beta-$decay and spontaneous fission (SF) of the isotopic chain of $Z=119$ superheavy nuclei under study is systematically analyzed within self-consistent relativistic mean field model. Moreover, our analysis confirmed that $\alpha-$decay is restricted within the mass range 284 $\leq$ A $\leq$ 296 and thus being the dominant decay channel in this mass range. However, for the mass range 297 $\leq$ A $\leq$ 375 the nuclei are unable to survive fission and hence SF is the principal mode of decay for these isotopes. There is no possibility of $\beta-$decay for the considered isotopic chain. In addition, we forecasted the mode of decay $^{284-296}$119 as one $\alpha$ chain from $^{284}$119 and $^{296}$119, two consistent $\alpha$ chains from $^{285}$119 and $^{295}$119, three consistent $\alpha$ chains from $^{286}$119 and $^{294}$119, four consistent alpha chains from $^{287}$119, six consistent alpha chains from $^{288-293}$119. Also from our analysis we inferred that for the isotopes $^{264-266,269}$Bh both $\alpha$ decay and SF are equally competent and can decay via either of these two modes. Thus, such studies can be of great significance to the experimentalists in very near future for synthesizing $Z=119$ superheavy nuclei.Comment: 14 pages, 6 figures. arXiv admin note: text overlap with arXiv:1611.00232, arXiv:1704.0315

Structural and decay properties of Z=132,138Z=132,138 superheavy nuclei

In this paper, we analyze the structural properties of $Z=132$ and $Z=138$ superheavy nuclei within the ambit of axially deformed relativistic mean-field framework with NL$3^{*}$ parametrization and calculate the total binding energies, radii, quadrupole deformation parameter, separation energies, density distributions. We also investigate the phenomenon of shape coexistence by performing the calculations for prolate, oblate and spherical configurations. For clear presentation of nucleon distributions, the two-dimensional contour representation of individual nucleon density and total matter density has been made. Further, a competition between possible decay modes such as $\alpha$-decay, $\beta$-decay and spontaneous fission of the isotopic chain of superheavy nuclei with $Z=132$ within the range 312 $\le$ A $\le$ 392 and 318 $\le$ A $\le$ 398 for $Z=138$ is systematically analyzed within self-consistent relativistic mean field model. From our analysis, we inferred that the $\alpha$-decay and spontaneous fission are the principal modes of decay in majority of the isotopes of superheavy nuclei under investigation apart from $\beta$ decay as dominant mode of decay in $^{318-322}138$ isotopes.Comment: 16 pages, 10 figures , 8 table

Commutativity of Addition in Prime Near-Rings with Right (θ,θ)-3-Derivations

Let N be a near-ring and  is a mapping on N . In this paper we introduce the notion of right ()-3-derivation in near-ring N. Also, we investigate the commutativity of addition of prime near-rings satisfying certain identities involving right ()-3-derivation

Jordan left (?,?) -derivations Of ?-prime rings

It was known that every left (?,?) -derivation is a Jordan left (?,?) – derivation on ?-prime rings but the converse need not be true. In this paper we give conditions to the converse to be true

SOME RESULTS OF GENERALIZED LEFT (θ,θ)-DERIVATIONS ON SEMIPRIME RINGS

Let R be an associative ring with center Z(R) . In this paper , we study the commutativity of semiprime rings under certain conditions , it comes through introduce the definition of generalized left(θ,θ)- derivation associated with left (θ,θ) -derivation , where Î¸ is a mapping on R

( U,R) STRONGLY DERIVATION PAIRS ON LIE IDEALS IN RINGS

Let R be an associative ring , U be a nonzero Lie ideal of R. In this paper , we will present the definition of (U,R) strongly derivation pair (d,g) , then we will get d=0 (resp. g=0 ) under  certain conditions on d and g for (U,R) strongly derivation pair (d,g) on semiprime ring . After that we will study prime rings , semiprime rings ,and rings  that have a commutator left nonzero divisor with (U,R) strongly derivation pair (d,g) , to obtain the notation of  (U,R) derivation

Jordan (θ, θ)*- Derivation Pairs of Rings With Involution

Let  R be a 6-torsion  free ring with involution , θ  is a mapping of R and let (d,g) : R→R be an additive mapping . In this paper  we will give the relation between (θ, θ)*-derivation pair and Jordan (θ, θ)*-derivation pair . Also , we will prove that if (d,g) is a Jordan (θ, θ)*-derivation pair , then d is a Jordan (θ, θ)*-derivation