Abstract:
This paper addresses scheduling a set of weighted jobs on a single machine in presence of release date for delivery in batches to customers or to other machines for further processing. The problem is a natural extension of minimizing the sum of weighted flow times by considering the possibility of delivering jobs in batches and introducing batch delivery costs. The classical problem is NP-hard and then the extended version of the problem is NP-hard. The objective function is that of minimizing the sum of weighted flow times and delivery costs. The extended problem arises in a real supply chain network by cooperation between two layers of chain. Structural properties of the problem are investigated and used to devise a branch-and-bound solution scheme. Computational experiments show the efficiency of suggested algorithm for solving instances up to 40 jobs.

Abstract:
We develop a general formalism to investigate the effect of quenched fixed charge disorder on effective electrostatic interactions between charged surfaces in a one-component (counterion-only) Coulomb fluid. Analytical results are explicitly derived for two asymptotic and complementary cases: i) mean-field or Poisson-Boltzmann limit (including Gaussian-fluctuations correction), which is valid for small electrostatic coupling, and ii) strong-coupling limit, where electrostatic correlations mediated by counterions become significantly large as, for instance, realized in systems with high-valency counterions. In the particular case of two apposed and ideally polarizable planar surfaces with equal mean surface charge, we find that the effect of the disorder is nil on the mean-field level and thus the plates repel. In the strong-coupling limit, however, the effect of charge disorder turns out to be additive in the free energy and leads to an enhanced long-range attraction between the two surfaces. We show that the equilibrium inter-plate distance between the surfaces decreases for elevated disorder strength (i.e. for increasing mean-square deviation around the mean surface charge), and eventually tends to zero, suggesting a disorder-driven collapse transition.

Abstract:
We investigate the non-perturbative results of multi-dimensional forced Burgers equation coupled to the continuity equation. In the inviscid limit, we derive the exact exponents of two-point density correlation functions in the universal region in arbitrary dimensions. We then find the universal generating function and the tails of the probability density function (PDF) for the longitudinal velocity difference. Our results exhibit that in the inviscid limit, density fluctuations affect the master equation of the generating function in such a way that we can get a positive PDF with the well-known exponential tail. The exponent of the algebraic tail is derived to be -5/2 in any dimension. Finally we observe that various forcing spectrums do not alter the power law behaviour of the algebraic tail in these dimensions, due to a relation between forcing correlator exponent and the exponent of the two-point density correlation function.

Abstract:
We investigate the effect of quenched surface charge disorder on electrostatic interactions between two charged surfaces in the presence of dielectric inhomogeneities and added salt. We show that in the linear weak-coupling regime (i.e., by including mean-field and Gaussian-fluctuations contributions), the image-charge effects lead to a non-zero disorder-induced interaction free energy between two surfaces of equal mean charge that can be repulsive or attractive depending on the dielectric mismatch across the bounding surfaces and the exact location of the disordered charge distribution.

Abstract:
The present study has been undertaken to evaluate the level of statistical competency of the post-graduate students belonging to the Faculty of Education in the Universities of Yemen and India. A standardized test prepared by the researchers has been used to assess the level of statistical competency of students. The study reveals that 1) The level of statistical competency of the post-graduate students belonging to the Faculty of Education in Universities of Yemen is average. 2) The level of statistical competency of the post-graduate students belonging to the Faculty of Education in Indian Universities is less than average. 3) The level of statistical competency of Yemeni post-graduate students is significantly higher than their counterparts of India. 4) There is a significant difference between male and female post-graduate students in the level of statistical competency. The male post-graduate students are better than female post-graduate students.

Abstract:
We address the critical and universal aspects of counterion-condensation transition at a single charged cylinder in both two and three spatial dimensions using numerical and analytical methods. By introducing a novel Monte-Carlo sampling method in logarithmic radial scale, we are able to numerically simulate the critical limit of infinite system size (corresponding to infinite-dilution limit) within tractable equilibration times. The critical exponents are determined for the inverse moments of the counterionic density profile (which play the role of the order parameters and represent the inverse localization length of counterions) both within mean-field theory and within Monte-Carlo simulations. In three dimensions (3D), correlation effects (neglected within mean-field theory) lead to an excessive accumulation of counterions near the charged cylinder below the critical temperature (condensation phase), while surprisingly, the critical region exhibits universal critical exponents in accord with the mean-field theory. In two dimensions (2D), we demonstrate, using both numerical and analytical approaches, that the mean-field theory becomes exact at all temperatures (Manning parameters), when number of counterions tends to infinity. For finite particle number, however, the 2D problem displays a series of peculiar singular points (with diverging heat capacity), which reflect successive de-localization events of individual counterions from the central cylinder. In both 2D and 3D, the heat capacity shows a universal jump at the critical point, and the energy develops a pronounced peak. The asymptotic behavior of the energy peak location is used to locate the critical temperature, which is also found to be universal and in accordance with the mean-field prediction.

Abstract:
Like-charged macroions attract each other as a result of strong electrostatic correlations in the presence of multivalent counterions or at low temperatures. We investigate the effective electrostatic interaction between i) two like-charged rods and ii) two like-charged spheres using the recently introduced strong-coupling theory, which becomes asymptotically exact in the limit of large coupling parameter (i.e. for large counterion valency, low temperature, or high surface charge density on macroions). Since we deal with curved surfaces, an additional parameter, referred to as Manning parameter, is introduced, which measures the ratio between the radius of curvature of macroions to the Gouy-Chapman length and controls the counterion-condensation process that directly affects the effective interactions. For sufficiently large Manning parameters (weakly-curved surfaces), we find a strong long-ranged attraction between two macroions that form a closely-packed bound state with small surface-to-surface separation of the order of the counterion diameter in agreement with recent simulations. For small Manning parameters (highly-curved surfaces), on the other hand, the equilibrium separation increases and the macroions unbind from each other as the confinement volume increases to infinity. This occurs via a continuous universal unbinding transition for two charged rods at a threshold Manning parameter of 2/3, while the transition is discontinuous for spheres because of a pronounced potential barrier at intermediate distances.

Abstract:
The counterion-condensation transition at charged cylinders is studied using Monte-Carlo simulation methods. Employing logarithmically rescaled radial coordinates, large system sizes are tractable and the critical behavior is determined by a combined finite-size and finite-ion-number analysis. Critical counterion localization exponents are introduced and found to be in accord with mean-field theory both in 2 and 3 dimensions. In 3D the heat capacity shows a universal jump at the transition, while in 2D, it consists of discrete peaks where single counterions successively condense.

Abstract:
Introduction: Our aim was to compare transabdominal ultrasonography (US) and intravenous urography (IVU) in the evaluation of patients with hematuria. Materials and Methods: Two hundred patients with hematuria were assessed by US and IVU, and if needed, by cystoscopy, ureteroscopy, and CT scan, to determine the definite cause of hematuria. The results of US and IVU were compared according to the definite diagnoses. Results: Of 97 patients with microscopic hematuria, 44 (45%) had a documented cause for hematuria, and of 103 patients with gross hematuria, 76 (74%) had a definite disorder (P < .001). Urinary calculi were found in 105 patients, 93 (88.5%) and 73 (69.5%) of which were detected by US and IVU, respectively (P < .001). There were 3 and 6 cases of kidney and bladder neoplasms, respectively, all of which were revealed by US, but only 2 renal tumors were detectable on IVU. Ultrasonography had a higher sensitivity than IVU for diagnoses of kidney calculi, lower ureteral calculi, and urologic neoplasms (95.3% versus 65.1% for kidney calculi, P = .039; 89.7% versus 69.2% for lower ureteral calculi, P < .001; and 100% versus 22.3% for urologic neoplasms, P < .001), but in calculi of the middle and upper ureter and of the whole ureter, there were no differences between US and IVU. Conclusion: Our results are in favor of using US in the initial evaluation of hematuria. However, we must choose our diagnostic tool according to the patient’s condition and suspected disorders causing hematuria.

Abstract:
Unemployment is an important issue in developing economies. High unemployment means that labor resources are not being used efficiently. In this research, the dynamic effects of unemployment rate on per capita real GDP in Iran are investigated during the period 1971 to 2006 using an Auto-Regressive Distributed Lag (ARDL). Also in this model, the physical capital, the consumer price index and the ratio of government expenditure to GDP as control variables have been considered. The findings show that the unemployment rate has a significant and negative effect on per capita real GDP in long-run and short-run. The value of error correction coefficient is equal to -0.48 implying that around 95% of the per capita real GDP adjustment occurs after two years.